Lawyers for President Donald Trump continued to argue that their "quintessentially federal dispute" belongs in federal court in a reply brief filed in the U.S. Court of Appeals for the Second Circuit late Thursday.

Trump sued Manhattan District Attorney Cyrus Vance Jr. in the Southern District of New York in September, arguing that Vance's office could not enforce a grand jury subpoena for eight years of Trump's tax returns.

Trump claimed that presidents are immune from state investigation and prosecution. He appealed to the Second Circuit after U.S. District Senior Judge Vincent Marrero dismissed the case, finding that federal courts shouldn't intervene in a state grand jury matter according to the 1971 U.S. Supreme Court decision Younger v. Harris.

Trump's legal team detailed their objections to Marrero's conclusion on the Younger doctrine in their reply brief, writing that Trump is claiming immunity from state process and that claim must be handled in federal court.

Younger also does not apply when the plaintiff is the federal government, according to the reply brief, which is signed by attorney William Consovoy of Consovoy McCarthy.

"The District Attorney no longer denies that the President is suing as President, that he represents the federal government here, that he is suing to enforce superior federal interests, or that the identity of his lawyers is irrelevant," Consovoy wrote. "The Justice Department — the entity normally responsible for representing the United States in court — also agrees that the President can claim this mantle."

Vance's lawyers have argued that grand jury proceedings are secret, comparing them to government tax agencies that have already seen the president's tax records. Consovoy dismissed that comparison in the reply brief.

"Regardless, disclosure to the District Attorney alone will harm the President because, unlike accountants and tax officials, the District Attorney is an adversary who is threatening to charge the President criminally and could use his information against him," Consovoy wrote.

Trump's lawyers filed two motions Tuesday asking for the current stay to be extended beyond the end of oral arguments to give Trump time to appeal to the Supreme Court, if the court's ruling is not in his favor. It's traditional for the Supreme Court to review claims of presidential immunity, Consovoy wrote in the reply brief.

Consovoy ended the reply brief by again calling for a stay pending appeal and later, if necessary, a stay pending certiorari. Vance's lawyers have argued they need this question to be resolved quickly due to statute-of-limitation issues with the related grand jury investigation. But appropriate resolution of the constitutional issues raised in this case is more important, Consovoy wrote.

Oral arguments are scheduled for Oct. 23.

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