
541 F.3d 476 (2008)
EMPRESA CUBANA DEL TABACO, doing business as Cubatabaco, Plaintiff-Counter-Defendant-Appellee,
v.
CULBRO CORPORATION, General Cigar Co., Inc. and General Cigar Holdings, Inc., Defendants-Counter-Claimants-Appellants,
Alfred Dunhill Ltd., Defendant.
Docket No. 07-1248-cv.
United States Court of Appeals, Second Circuit.
Argued: August 4, 2008.
Decided September 4, 2008.
*477 Andrew L. Deutsch, DLA Piper U.S. LLP (Joshua S. Sohn, DLA Piper U.S. LLP, Harry C. Marcus and Scott Greenberg, Morgan & Finnegan, LLP, of counsel), New York, NY, for Defendants-Counter-Claimaints-Appellants.
Michael Krinsky (David B. Goldstein, Christopher J. Klatell, on the brief), Rabinowitz, Boudin, Standard, Krinsky & Lieberman, P.C., New York, NY, for Plaintiff-Counter-Defendant-Appellee.
Before: RAGGI, WESLEY, LIVINGSTON, Circuit Judges.
PER CURIAM:
Defendants-counter-claimants-appellants Culbro Corporation, General Cigar Co., Inc., and General Cigar Holdings, Inc. (collectively, "General Cigar") appeal from a March 14, 2007 order of the District Court for the Southern District of New York (Sweet, J.) denying a motion for an order directing the United States Patent and Trademark Office ("PTO") to dismiss the pending petitions of plaintiff-counter-defendant-appellee Empresa Cubana del Tabaco ("Cubatabaco") to cancel General Cigar's registration of the COHIBA trademark for cigars sold in the United States, and to register the mark in Cubatabaco's name. See Empresa Cubana Del Tabaco v. Culbro Corp., 478 F.Supp.2d 513 (S.D.N.Y.2007). Because we conclude that the district court did not abuse its discretion in denying the relief requested, we affirm.

BACKGROUND
This case arises from a dispute over the ownership of the COHIBA mark on cigars sold in the United States. That dispute and much of the relevant procedural history leading up to this appeal are described in detail in Empresa Cubana del Tabaco v. Culbro Corp., 399 F.3d 462 (2d Cir.2005) ("Empresa V"), familiarity with which is assumed.
Following our decision in Empresa V, the district court issued an order dated May 15, 2006 dismissing all remaining claims in this case, as required by our mandate. On July 6, 2006, General Cigar filed a motion in the district court requesting:
an order pursuant to 15 U.S.C. § 1119 and the ancillary jurisdiction of the Court, amending the Court's order of May 15, 2006 so as to direct the Director of the [PTO] to (1) dismiss the pending petition of [Cubatabaco] in the [PTO]... which seeks cancellation of General Cigar's United States Trademark Registrations... for COHIBA, and (2) dismiss Cubatabaco's pending application before the [PTO] to register the COHIBA mark in its own name; or, in the alternative, entering final judgment that grants such relief in addition to dismissing all remaining claims.
*478 By order dated March 14, 2007, the district court denied the July 6, 2006 motion. See Empresa Cubana Del Tabaco, 478 F.Supp.2d 513. General Cigar now appeals.

DISCUSSION
The kind of relief General Cigar requested is authorized by 15 U.S.C. § 1119. That statute provides that:
In any action involving a registered mark the court may determine the right to registration, order the cancelation of registrations, in whole or in part, restore canceled registrations, and otherwise rectify the register with respect to the registrations of any party to the action. Decrees and orders shall be certified by the court to the Director [of the PTO], who shall make appropriate entry upon the records of the Patent and Trademark Office, and shall be controlled thereby.
15 U.S.C. § 1119. General Cigar did not request section 1119 relief as a counterclaim, but only as part of its July 6, 2006 motion, following the adjudication of the underlying trademark dispute and the district court's dismissal of the action. For this reason, the district court treated the July 6, 2006 motion as one to amend the judgment under Federal Rule of Civil Procedure 59(e). General Cigar concedes that this was an appropriate interpretation.
"A district court's denial of a party's motion to alter or amend judgment under Rule 59(e) is ... reviewed for an abuse of discretion." Munafo v. Metro. Transp. Auth., 381 F.3d 99, 105 (2d Cir. 2004). Furthermore, the ultimate decision as to whether to grant the kind of relief sought by General Cigar is committed to the discretion of the district court. This is demonstrated by section 1119's use of the permissive "may" in authorizing courts to grant relief, as distinct from its use of the mandatory "shall" in requiring any orders or decrees that are entered to be sent to and followed by the PTO. See Jama v. Immigration & Customs Enforcement, 543 U.S. 335, 346, 125 S.Ct. 694, 160 L.Ed.2d 708 (2005) ("The word `may' customarily connotes discretion. That connotation is particularly apt where ... `may' is used in contraposition to the word `shall.'" (citation omitted)); see also, e.g., Atsilov v. Gonzales, 468 F.3d 112, 116 (2d Cir.2006) (where statute used permissive "may" instead of mandatory "shall" in authorizing agency to grant relief, the "ultimate decision whether to grant relief [was] entrusted to the discretion of the [agency]"). Accordingly, we review the district court's decision in this case not to amend the judgment to include section 1119 relief for an abuse of discretion. See, e.g., Cent. Mfg., Inc. v. Brett, 492 F.3d 876, 883 (7th Cir.2007).
Rule 59(e) permits a party to seek amendment of a judgment no later than ten days after the judgment is entered. See Fed.R.Civ.P. 59(e). The parties dispute when and whether judgment actually was entered in this case, and therefore whether the July 6, 2006 motion was timely. We decline to reach the timeliness issue, however, because we are persuaded that the district court did not abuse its discretion in denying the motion on the merits.
A request for dismissal of a cancellation proceeding pursuant to section 1119 ordinarily is made as a counterclaim in an infringement action. See, e.g., Avon Shoe Co. v. David Crystal, Inc., 279 F.2d 607, 609, 614-15 (2d Cir.1960) (involving counterclaim by defendants in a trademark infringement action); see also Nasalok Coating Corp. v. Nylok Corp., 522 F.3d 1320, 1325 (Fed.Cir.2008) ("[Section 1119] allows a trademark infringement defendant *479 to assert a counterclaim to cancel the registration."); Eagles, Ltd. v. Am. Eagle Found., 356 F.3d 724, 730-31 (6th Cir. 2004) (because defendant "failed to raise the [section 1119] argument as a counterclaim to the infringement action," the question whether relief should be granted was not "properly before the district court"); Thomas J. McCarthy, McCarthy on Trademarks and Unfair Competition (4th ed.2008) § 30:108 (noting that a "defendant charged with infringement of a registered mark may counterclaim for cancellation of that registration" under section 1119). As the Sixth Circuit stated in Eagles, when such a request is made for the first time after the underlying trademark dispute has been adjudicated, it is properly construed as being based on an estoppel theory. That is, a request for section 1119 relief made for the first time after judgment essentially amounts to a claim that because the district court adjudicated a trademark case in a certain way, there is nothing left for the PTO to decide, and so it ought to be instructed to follow the court's lead for the sake of efficiency and consistency. See Eagles, 356 F.3d at 731. Like the Sixth Circuit in Eagles, we see no reason why it was an abuse of discretion for the district court simply to tell General Cigar to raise its estoppel claim before the PTO and let the agency decide, subject to review by the Federal Circuit, what preclusive effect should be given to our decision in Empresa V, if any. See id. (noting PTO's expertise in addressing the estoppel issue).
Insofar as General Cigar contends that its July 6, 2006 motion was not one to amend the judgment, but rather one to enforce the judgment pursuant to the district court's ancillary jurisdiction, our conclusion is the same. Although the Supreme Court has "reserved the use of ancillary jurisdiction in subsequent proceedings for the exercise of a federal court's inherent power to enforce its judgments," Peacock v. Thomas, 516 U.S. 349, 356, 116 S.Ct. 862, 133 L.Ed.2d 817 (1996), it has "cautioned against the exercise of jurisdiction over proceedings that are entirely new and original or where the relief [sought is] of a different kind or on a different principle than that of the prior decree," id. at 358, 116 S.Ct. 862 (citation and internal quotation marks omitted; alteration in original). These principles counsel against the exercise of ancillary jurisdiction in this case. Because General Cigar did not raise its section 1119 claim in the pleadings, the question whether relief should be granted was not before this Court in Empresa V, nor before the district court when it entered the May 15, 2006 order dismissing all remaining claims. Hence, the relief sought here is "of a different kind," id., than what was considered in connection with Empresa V. And because the July 6, 2006 motion is properly construed as being based on an estoppel theory, it is premised on a "different principle than that of the prior decree," id., which was based on a consideration of the merits. Accordingly, the July 6, 2006 motion was not a proper invocation of the district court's ancillary enforcement jurisdiction.
We have considered General Cigar's remaining arguments and conclude that they are without merit. The judgment of the district court hereby is AFFIRMED.
