delivered the opinion of the Court.

The Major Crimes Act of 1885 1 authorizes the prosecution in federal court of an Indian charged with the com*206mission on an Indian reservation of certain specifically-enumerated offenses.2 This case requires us to decide whether an Indian prosecuted under the Act is entitled to a jury instruction on a lesser included offense where that lesser offense is not one of the crimes enumerated in the Act.

At the close of petitioner’s trial for assault with intent to commit serious bodily injury, the United States District Court for the District of South Dakota refused to instruct the jury, as petitioner requested, that they might convict him of simple assault. The court reasoned that since simple assault is not an offense enumerated in the Act, it is exclusively “a matter for the tribe.” App. 15. A panel of the United States Court of Appeals for the Eighth Circuit, one judge dissenting, upheld that determination on the strength of the court’s earlier de~ *207cisión in Kills Crow v. United States, 451 F. 2d 323 (1971). 459 F. 2d 757 (1972). Following a remand to the District Court for a hearing on an unrelated issue,3 the case returned to the Court of Appeals and the conviction was affirmed. Id., at 762 (supplemental opinion). We granted certiorari limited to the question of the validity of denying the requested instruction,4 409 U. S. 1037 (1972), and we reverse.

The events that led to the death of petitioner’s brother-in-law, Robert Pomani, and hence to this criminal prosecution, took place on the South Dakota Reservation of the Crow Creek Sioux Tribe. Petitioner and the deceased, both Indians of that Tribe, spent the evening of March 6, 1971, drinking and quarreling over petitioner’s alleged mistreatment of his wife, Pomani’s sister. The argument soon became violent, and it ended only when petitioner, having beaten Pomani severely and left him bleeding from the head and face, went to bed. The next morning he discovered Pomani’s lifeless body on the ground a short distance from the house where the beating had occurred. He reported the death to an official of the Department of the Interior serving as Captain of the Tribal Police at Fort Thompson, South Dakota. An autopsy revealed that Pomani died because of exposure to excessive cold, although the beating was a contributing factor. Petitioner was convicted of assault with intent to inflict great bodily injury, and sentenced to five years’ imprisonment.

*208Although the lesser included offense doctrine developed at common law to assist the prosecution in cases where the evidence failed to establish some element of the offense originally charged,5 it is now beyond dispute that the defendant is entitled to an instruction on a lesser included offense if the evidence would permit a jury rationally to find him guilty of the lesser offense and acquit him of the greater. The Federal Rules of Criminal Procedure deal with lesser included offenses, see Rule 31 (c),6 and the defendant’s right to such an instruction has been recognized in numerous decisions of this Court. See, e. g., Sansone v. United States, 380 TJ. S. 343, 349 (1965); Berra v. United States, 351 U. S. 131, 134 (1956); Stevenson v. United States, 162 U. S. 313 (1896).7

In defending the trial court’s refusal to offer the requested instruction, the Government does not dispute this general proposition, nor does it argue that a lesser offense instruction was incompatible with the evidence presented at trial. Cf. Sansone v. United States, supra; Sparf v. United States, 156 U. S. 51, 63-64 (1895). On the contrary, the Government explicitly concedes that any non-Indian who had committed this same act on this same reservation and requested this same *209instruction would have been entitled to the jury charge that petitioner was refused. Brief for the United States 13 n. 16.8 The Government does maintain, however, that the Major Crimes Act precludes the District Court from offering a lesser offense instruction on behalf of an Indian, such as the petitioner before us. Specifically, the Government contends that the Act represents a carefully limited intrusion of federal power into the otherwise exclusive jurisdiction of the Indian tribes to punish Indians for crimes committed on Indian land. To grant an instruction on the lesser offense of simple assault would, in the Government’s view, infringe the tribe’s residual jurisdiction in a manner inconsistent with the Act. Under the Government’s approach, in other words, the interests of an individual Indian defendant in obtaining a jury instruction on a lesser offense must fall before the congressionally sanctioned interests of the tribe in preserving its inherent jurisdiction. Since that conclusion is compelled neither by the language, nor the purposes, nor the history of the Act, we cannot agree.

The Major Crimes Act was passed by Congress in direct response to the decision of this Court in Ex parte Crow Dog, 109 U. S. 556 (1883). The Court held there that a federal court lacked jurisdiction to try an Indian for the murder of another Indian, a chief of the Brule Sioux named Spotted Tail, in Indian country. Although recognizing the power of Congress to confer such jurisdiction on the federal courts,9 the Court reasoned that, in *210the absence of explicit congressional direction, the Indian tribe retained exclusive jurisdiction to punish the offense. Cf. Taitón v. Mayes, 163 U. S. 376 (1896); Worcester v. Georgia, 6 Pet. 515 (1832).

The prompt congressional response — conferring jurisdiction on the federal courts to punish certain offenses— reflected a view that tribal remedies were either nonexistent or incompatible with principles that Congress thought should be controlling. Representative Cutcheon, sponsor of the Act, described the events that followed the reversal by this Court of Crow Dog's conviction:

“Thus Crow Dog went free. He returned to his reservation, feeling, as the Commissioner says, a great deal more important than any of the chiefs of his tribe. The result was that another murder grew out of that — a murder committed by Spotted Tail, jr., upon White Thunder. And so these things must go on unless we adopt proper legislation on the subject.

“It is an infamy upon our civilization, a disgrace to this nation, that there should be anywhere within its boundaries a body of people who can, with absolute impunity, commit the crime of murder, there being no tribunal before which they can be brought for punishment. Under our present law there is no penalty that can be inflicted except according to the custom of the tribe, which is simply that the 'blood-avenger' — that is, the next of kin to the person murdered — shall pursue the one who has been guilty of the crime and commit a new murder upon him. . . .

“If ... an Indian commits a crime against an Indian on an Indian reservation there is now no law to punish the offense except, as I have said, the *211law of the tribe, which is just no law at all.” 16 Cong. Rec. 934 (1885).10

The Secretary of the Interior, who supported the Act, struck a similar note:

“If offenses of this character [the killing of Spotted Tail] can not be tried in the courts of the United States, there is no tribunal in which the crime of murder can be punished. Minor offenses may be punished through the agency of the ‘court of Indian offenses,' but it will hardly do to leave the punishment of the crime of murder to a tribunal that exists only by the consent of the Indians of the reservation. If the murderer is left to be punished according to the old Indian custom, it becomes the duty of the next of kin to avenge the death of his relative by either killing the murderer or some one of his kinsmen . . . .”11

In short, Congress extended federal jurisdiction to crimes committed by Indians on Indian land out of a conviction that many Indians would “be civilized a great deal sooner by being put under [federal criminal] laws and taught to regard life and the personal property of *212others.” 16 Cong. Rec. 936 (1885) (remarks of Rep. Cutcheon). That is emphatically not to say, however, that Congress intended to deprive Indian defendants of procedural rights guaranteed to other defendants, or to make it easier to convict an Indian than any other defendant. Indeed, the Act expressly provides that Indians charged under its provisions “shall be tried in the same courts, <md in the same manner,, as are all other persons committing any of the above crimes within the exclusive jurisdiction of the United States.” 18 U. S. C. § 3242 (emphasis added).12 In the face of that explicit statutory direction, we can hardly conclude that Congress intended to disqualify Indians from the benefits of a lesser offense instruction, when those benefits are made available to any non-Indian charged with the same offense.

Moreover, it is no answer to petitioner’s demand for a jury instruction on a lesser offense to argue that a defendant may be better off without such an instruction. True, if the prosecution has not established beyond a reasonable doubt every element of the offense charged, and if no lesser offense instruction is offered, the jury must, as a theoretical matter, return a verdict of acquittal. But a defendant is entitled to a lesser offense instruction — in this context or any other — precisely because he should not be exposed to the substantial risk that the jury’s practice will diverge from theory. Where one of *213the elements of the offense charged remains in doubt, but the defendant is plainly guilty of some offense, the jury is likely to resolve its doubts in favor of conviction. In the case before us, for example, an intent to commit serious bodily injury is a necessary element of the crime with which petitioner was charged, but not of the crime of simple assault. Since the nature of petitioner's intent was very much in dispute at trial, the jury could rationally have convicted him of simple assault if that option had been presented. But the jury was presented with only two options: convicting the defendant of assault with intent to commit great bodily injury, or acquitting him outright. We cannot say that the availability of a third option — convicting the defendant of simple assault — could not have resulted in a different verdict. Indeed, while we have never explicitly held that the Due Process Clause of the Fifth Amendment guarantees the right of a defendant to have the jury instructed on a lesser included offense, it is nevertheless clear that a construction of the Major Crimes Act to preclude such an instruction would raise difficult constitutional questions. In view of our interpretation of the Act, those are questions that we need not face.13

*214Finally, we emphasize that our decision today neither expands the reach of the Major Crimes Act nor permits the Government to infringe the residual jurisdiction of a tribe by bringing prosecutions in federal court that are not authorized by statute.14 We hold only that where an Indian is prosecuted in federal court under the provisions of the Act, the Act does not require that he be deprived of the protection afforded by an instruction on a lesser included offense, assuming of course that the evidence warrants such an instruction. No interest of a tribe is jeopardized by this decision. Accordingly, the judgment of the Court of Appeals is reversed and the case is remanded for further proceedings consistent with this opinion.

Reversed and remanded.

with whom Mr. Justice Powell and Mr. Justice Rehnquist join, dissenting.

As the opinion of the Court demonstrates, the Major Crimes Act, 18 U. S. C. §§ 1153, 3242, was enacted in response to this Court’s decision in Ex -parte Crow Dog, 109 U. S. 556. The Act conferred jurisdiction upon federal district courts over certain enumerated crimes committed by Indians on an Indian reservation, leaving tribal jurisdiction intact as to all other crimes. An Indian tried in a federal court under the Act is guaranteed equal procedural rights, 18 U. S. C. § 3242, including the benefits and burdens of Fed. Rule Crim. Proc. 31 (c), dealing with a lesser included offense.

In these respects, I agree with the Court. But the Court goes on to hold “that where an Indian is prosecuted in federal court under the provisions of the Act, the Act does not require that he be deprived of the protection afforded by an instruction on a lesser included offense. . . .” Ante, at 214. I think this holding would be correct only if the lesser included offense were one over which the federal court had jurisdiction. Because the trial court did not have jurisdiction over the “lesser included offense” in the present case, I must respectfully dissent.1

It is a commonplace that federal courts are courts of limited jurisdiction, and that there are no common-law offenses against the United States. “The legislative authority of the Union must first make an act a crime, affix a punishment to it, and declare the Court that shall have jurisdiction of the offence.” United States v. Hudson, 7 Cranch 32, 34. “It is axiomatic that statutes creating and defining crimes cannot be extended by intendment, and that no act, however wrongful, can be punished under such a statute unless clearly within its terms.” *216Todd v. United States, 158 U. S. 278, 282. See 1 J. Moore, Federal Practice ¶ 0.60 [7]. And it is also clear that simple assault by an Indian on an Indian reservation, the purported “lesser included offense” in this case, comes within no federal jurisdictional statute. The Court in effect holds that Fed. Rule Crim. Proc. 31 (c) implicitly operates to confer federal jurisdiction over simple assault in the circumstances of this case, and with all respect this seems to me a holding utterly without support.

The Rule states that:

“The defendant may be found guilty of an offense necessarily included in the offense charged or of an attempt to commit either the offense charged or an offense necessarily included therein if the attempt is an offense.” (Emphasis added.)

The Rule is thus phrased in terms of “offenses.” It seems to me clear that “offense” means federal offense, and this view is confirmed by the fact that by virtue of the Rule a lesser included offense instruction is authorized with respect to “an attempt” only where the attempt itself is also a federal crime.

The conclusion that a lesser included offense instruction is possible only when the lesser offense is within federal jurisdiction does not violate 18 U. S. C. § 3242, providing that Indians charged under its provisions “shall be tried in the same courts, and in the same manner, as are all other persons committing any of the above crimes within the exclusive jurisdiction of the United States.” For this conclusion would apply as well in any instance where Congress has established a divided criminal jurisdiction between a federal district court and another forum. See, e. g., DeFlumer v. Mancusi, 443 F. 2d 940 (criminal jurisdiction in federal district court over 16-year-old defendants only when charged with certain enumerated crimes). Congress established jurisdiction *217in the federal district courts only over certain specifically enumerated offenses committed by Indians on Indian reservations. It vested a residual jurisdiction in other forums over all other offenses. Accordingly, I conclude that a lesser included offense instruction would have been improper in the present case, where the federal court had no jurisdiction over the lesser offense of simple assault.2 See Kills Crow v. United States, 451 F. 2d 323, 325.

The Court seems to agree that a United States Attorney could not seek an indictment in a federal district court of an Indian for simple assault committed on an Indian reservation. This being so, I can find no basis for concluding that jurisdiction comes into being simply by-motion of the defense. “It needs no citation of authorities to show that the mere consent of parties cannot confer upon a court of the United States the jurisdiction to hear and decide a case.” People’s Bank v. Calhoun, 102 U. S. 256, 260-261. See also 1 J. Moore, Federal Practice ¶ 0.60 [4]. Were the petitioner’s motion for an instruction on simple assault to be granted, and were a jury to convict on that offense, I should have supposed until the Court’s decision today that the conviction could have been set aside for want of jurisdiction.