Petitioner Franklin Grullon moves to dismiss these proceedings without prejudice. In October 2003, Grullon, who already had two 28 U.S.C. § 2241 petitions pending in the federal courts, filed a third § 2241 petition, challenging his conviction on the grounds that: (1) he was misled into pleading guilty; (2) his conviction was not final for deportation purposes because he is actually innocent; (3) even if he is deportable, he is entitled to apply for a waiver of deportation; and (4) he was deprived of due process during his removal proceedings. The United States District Court for the Eastern District of New York (Trager, J.) construed Grullon’s October 2003 28 U.S.C. § 2241 petition as a 28 U.S.C. § 2255 petition, and determined that because Grullon previously had filed a § 2255 petition in the Southern District of New York, the October 2003 petition should be treated as a successive § 2255 petition and transferred to this Court for certification for appeal. Because the October 2003 petition presented claims recognized by both §§ 2241 and 2255, however, we hold that the district court erred in construing the entire petition as a successive § 2255 petition. We find that Grul-lon’s claim that he was denied due process during his removal proceedings was the proper subject of a § 2241 petition. Where, as here, an additional § 2241 petition is filed before the complete disposition of a prior § 2241 petition, we hold that the principles enunciated in Ching v. United States, 298 F.3d 174 (2d Cir. 2002), are applicable. Applying Ching’s rationale, the subsequently-filed § 2241 petition should be construed as a motion to amend a pending § 2241 petition. See id. at 177-78. Accordingly, Grullon’s claim that he was denied due process at his removal proceedings is remanded to the United States District Court for the Eastern District of New York for consideration as a motion to amend the § 2241 petition pending in that court. Petitioner’s remaining claims are dismissed without prejudice.

BACKGROUND

Following a 1996 conviction for an aggravated felony involving controlled substances, the Immigration and Naturaliza*139tion Service (“INS”) initiated removal proceedings against Grullon, charging that he was a removable alien. In August 1998, an immigration judge ordered Grul-lon removed from the United States, finding him ineligible for relief under § 212(c) of the Immigration and Nationality Act (“INA”), 8 U.S.C. § 1182(c).

In November 2001, Grullon filed a § 2241 petition in the Eastern District of New York, challenging the INS’s authority to detain him and seeking an order enjoining the INS from asserting that he was ineligible for relief under § 212(c). The district court granted the petition in December 2002 and the government subsequently appealed that decision. That appeal is currently pending in this Court.

In September 2003, Grullon filed another § 2241 petition in the Eastern District of New York, challenging his detention under § 236(c) of the INA. That petition is currently pending in the district court. In October 2003, Grullon filed the instant § 2241 petition in the Eastern District of New York, arguing that the removal proceedings against him should be terminated because: (1) he was misled into pleading guilty; (2) his conviction is not final for immigration purposes; (3) even if he is deportable, he is entitled to apply for a § 212(c) waiver of deportation; and (4) the government engaged in “affirmative misconduct” during the removal proceedings, which deprived him of due process during those proceedings. In reviewing the instant petition, the district court concluded that “[t]he crux of [the] instant petition is his claim that he was promised he would not be deported if he pleaded guilty,” and therefore the petition challenged his underlying conviction and sentence, rather than the execution of his sentence. See Order, 03-CV-5179(DGT) (E.D.N.Y. Oct. 30, 2003). Accordingly, the district court construed the instant § 2241 petition as a § 2255 petition, and noted that because Grullon previously filed an unsuccessful § 2255 petition in the Southern District of New York, the instant petition should be treated as a successive § 2255 petition and transferred to this Court for certification to appeal, pursuant to Liriano v. United States, 95 F.3d 119, 122-23 (2d Cir. 1996).

Grullon then filed the instant motion to dismiss this proceeding without prejudice, asserting that he is ineligible for § 2255 habeas relief because he is no longer in custody pursuant to his federal conviction, and arguing that the proper forum for his claims is a petition for a writ of error coram nobis.

DISCUSSION

A § 2241 petition generally challenges the execution of a federal prisoner’s sentence, whereas challenges to the underlying conviction and sentence are properly raised in a § 2255 petition. Jiminian v. Nash, 245 F.3d 144, 146-47 (2d Cir. 2001). When a district court is presented with a § 2241 petition raising claims that are properly the subject of a § 2255 petition, it may construe the petition as a successive habeas petition and transfer it to this Court, without giving prior notice to the petitioner, so long as the petitioner’s earlier § 2255 petition was dismissed on the merits. See id. at 148.

Here, however, the district court erred in construing Grullon’s entire petition as a § 2255 petition. Although some of Grullon’s claims challenged the validity of his guilty plea, and therefore were within the ambit of § 2255, he also claimed deprivation of due process during his removal proceedings. It is well settled that a claim concerning deprivation of due process during removal proceedings is properly the subject of a § 2241 petition. See, e.g., Brown v. Ashcroft, 360 F.3d 346 (2d Cir. 2004) (resolving due process claims *140presented in a § 2241 habeas petition); Liu v. INS, 293 F.3d 36 (2d Cir. 2002) (same). Accordingly, only those claims concerning Grullon’s underlying conviction and sentence should have been construed as a § 2255 petition. We are then left with the question of how to treat Grullon’s remaining § 2241 due process claim, given that he has § 2241 petitions pending in both this Court and the Eastern District of New York.

It is unclear whether a § 2241 claim is subject to the restrictions on successive petitions imposed by the Antiterrorism and Effective Death Penalty Act, 28 U.S.C. § 2244 (2004), as this Court has not yet decided “whether, in what circumstances, and under what constraints a petitioner may bring a second or successive § 2241 petition.” Simon v. United States, 359 F.3d 139, 143 (2d Cir. 2004).1 Nevertheless, we need not decide this question in the instant motion. Even if the restrictions on filing successive habeas petitions extended to § 2241 petitions, Grullon’s § 2241 due process petition should not be considered successive, as he has a prior § 2241 petition pending in the Eastern District of New York, and an appeal from a grant of another § 2241 petition pending in this Court. In Ching v. United States, 298 F.3d 174 (2d Cir. 2002), this Court held that when a second § 2255 petition is filed before the adjudication of the initial § 2255 petition, which includes an appeal from the decision on the petition, the second petition is not characterized as a successive § 2255 petition, but rather should be construed as a motion to amend the pending § 2255 petition. Id. at 177-78. We have applied similar principles in the context of § 2254 petitions, see Littlejohn v. Artuz, 271 F.3d 360, 363 (2d Cir. 2001), and we now hold that Ching’s rationale is applicable in the context of § 2241 petitions as well. Accordingly, we construe the instant § 2241 petition as a motion to amend.

We deny certification of those claims properly presented in Grullon’s § 2255 petition and subsequently transferred to this Court on the ground that Grullon is no longer in custody pursuant to his federal conviction and therefore is no longer eligible for '§ 2255 habeas relief. As we have stated previously, Grullon’s due process claim was properly the subject of a § 2241 petition, and should now, in keeping with Ching, be construed as a motion to amend. Accordingly, we remand Grullon’s § 2241 due process claim to the district court be treated as a motion to amend.

CONCLUSION

We deny the motion for certification for leave to appeal the claims properly raised in the § 2255 petition without prejudice to petitioner to raise these claims in the appropriate manner. With regard to petitioner’s due process claim, we hold that this claim was properly the subject of a § 2241 petition, and, pursuant to Ching, should be construed as a motion to amend. We therefore remand the § 2241 petition to the district court for consideration in conformity with this opinion.