OPINION

Samuel Muniz, a federal prisoner incarcerated at FCI Fort Dix, appeals an order denying his 28 U.S.C. § 2241 habeas corpus petition. We will affirm.

Muniz filed his petition in May 2010, accusing the Bureau of Prisons (BOP) of erring in its calculation of his term of incarceration. However, upon reviewing the sentence prior to filing its reply, the BOP determined that Muniz was entitled to the requested adjustment. It therefore revised Muniz’s term of incarceration to provide credit for the time he had spent in state custody from June 9, 1999, through July 10, 2001, pursuant to U.S.S.G. § 5G1.3. As Muniz “ha[d] received the re *166 lief he seeks and the Petition no longer presented] a live case or controversy,” the Government asked for the District Court to dismiss the petition as moot, and the District Court obliged.

Shortly thereafter, Muniz submitted a document entitled “Petitioner’s Informative Motion and Request for Determination,” in which, inter alia, he further challenged his revised term of incarceration because “the BOP failed to credit good conduct time from June 9, 1999.” Determining that this ground should have been raised in a new petition, the District Court simultaneously opened a new docket 1 and denied the new petition without prejudice as unexhausted. See Muniz v. Zickefoose, No. 10-2444, 2011 WL 3022439, at *4-5 (D.N.J. July 21, 2011). A timely notice of appeal followed. 2

We have jurisdiction pursuant to 28 U.S.C. §§ 1291 3 and 2253. Our review of the District Court’s legal conclusions is plenary. See Rios v. Wiley, 201 F.3d 257, 262 (3d Cir. 2000). “A challenge to the BOP’s execution of a sentence is properly brought under 28 U.S.C. § 2241.” Burkey v. Marberry, 556 F.3d 142, 146 (3d Cir. 2009).

First, we agree with the District Court that Muniz’s post-dismissal filing was properly construed as a new petition. The claims raised were altogether new— indeed, they arose from Muniz’s success in achieving relief under his first petition. The District Court appropriately determined that “what [Muniz] filed as the Motion in this action should have been filed— after due administrative exhaustion — as a new and separate § 2241 petition.” Muniz, 2011 WL 3022439, at *4.

Federal prisoners are ordinarily required to exhaust available administrative remedies before seeking relief under § 2241. Moscato v. Fed. Bureau of Prisons, 98 F.3d 757, 760 (3d Cir. 1996); see also Rogers v. United States, 180 F.3d 349, 358 & n. 16 (1st Cir. 1999); Little v. Hopkins, 638 F.2d 953, 953-54 (6th Cir. 1981) (per curiam). In order to exhaust, petitioners must satisfy the procedural requirements of the administrative remedy process. 4 Moscato, 98 F.3d at 761-62. Muniz argues that he did exhaust by lodging the complaints that gave rise to his initial § 2241 petition, but we do not agree; as the specific sentence-calculation issue, involving good-conduct-time credits, arose only after the filing of the first petition, the BOP could not have been on notice of the problem and was therefore unable to apply its expertise to it. See Moscato, 98 F.3d at 761-62 (explaining why exhaustion is required under § 2241). Nor has Muniz shown that exhaustion would be futile and hence excused. See Gambino v. Morris, 134 F.3d 156, 171 (3d Cir. 1998); see also Fazzini v. N.E. Ohio Corr. Ctr., 473 F.3d 229, 236 (6th Cir. 2006) (“[A] habeas petitioner’s failure to complete the administrative remedy process may be excused where his failure is due to the administra *167 tor, rather than the petitioner....”). That the Government’s counsel believes the law to require a contrary outcome does not excuse Muniz from pursuing the administrative remedies the BOP makes available, and Muniz has not otherwise demonstrated that the “purposes of exhaustion would not be served here.” Woodall v. Fed. Bureau of Prisons, 432 F.3d 235, 239 n. 2 (3d Cir. 2005).

Nor do we detect any error in the District Court’s procedural approach. The Government properly raised the affirmative defense of exhaustion in opposition to Muniz’s “motion.” Winck v. England, 327 F.3d 1296, 1304 n. 6 (11th Cir. 2003). And despite being given “thirty days” from dismissal to show exhaustion and reopen proceedings, see Muniz, 2011 WL 3022439, at *5, Muniz did not timely do so. Cf. Landano v. Rafferty, 897 F.2d 661, 668 (3d Cir. 1990) (“[A] habeas petitioner bears the burden of proving that he has exhausted available ... remedies.”).

In sum, we agree with the District Court’s decision to dismiss the case without prejudice, and we will affirm its judgment. Should Muniz eventually exhaust the available administrative remedies — and his submissions to this Court suggest that his efforts to exhaust may still be ongoing — he may file a new petition at that time in compliance with all applicable rules.