WASHINGTON — In a pair of filings on Thursday, a House committee and Manhattan prosecutors urged the Supreme Court to clear the way for disclosure of President Trump’s financial records.

The filings concerned subpoenas in separate cases to Mr. Trump’s accounting firm, Mazars USA. Federal appeals courts have refused to block the subpoenas, and the firm has indicated that it will provide the requested records unless the Supreme Court orders it to withhold them.

In one Supreme Court brief, the House Oversight and Reform Committee opposed an emergency application from Mr. Trump to block a subpoena seeking his financial records while the court decides whether to hear his appeal.

“Each day of delay,” the brief said, “harms Congress by depriving it of important information it needs to carry out its constitutional responsibilities.”

Mr. Trump’s application, filed last week, sought a stay of a ruling in October by a divided panel of the United States Court of Appeals for the District of Columbia Circuit rejecting the president’s argument that the subpoena was improper because the committee had no valid legislative purpose for seeking the information. “Having considered the weighty interests at stake in this case, we conclude that the subpoena issued by the committee to Mazars is valid and enforceable,” Judge David S. Tatel wrote for the majority.

Responding to Mr. Trump’s request in Thursday’s filing, lawyers for the committee said its inquiries were driven by its legislative and oversight responsibilities.

“Among other issues,” the brief said, “the committee is investigating whether senior government officials, including the president, are acting in the country’s best interest and not in their own financial interest, whether federal agencies are operating free from financial conflicts and with accurate information, and whether any legislative reforms are needed to ensure that these fundamental principles are respected.”

When the subpoena was issued in April, the House had not yet voted to pursue an impeachment inquiry. Now that it has, the brief said, the “rapidly advancing impeachment inquiry also makes it particularly important that Congress not be deprived of the information sought by the subpoena.”

“It matters little,” the brief said, “that the committee did not originally seek the information in question pursuant to the House’s impeachment power. Now that the House is exercising its grave constitutional responsibilities under that power, it should be fully informed with all the information to which it is entitled — including information it had previously sought for legislative purposes.”

On Monday, Chief Justice John G. Roberts Jr. issued a temporary stay to give the court time to consider Mr. Trump’s application for a longer one. Should the Supreme Court deny the application in the case, Trump v. Mazars USA, No. 19A545, the accounting firm would be required to provide the requested records.

If the Supreme Court grants the application and issues a stay, the committee’s lawyers wrote, it should require Mr. Trump’s lawyers to file a petition seeking review of the appeals court’s ruling by Dec. 2. That would allow the court to announce whether it will hear the case in the coming weeks and to render a decision by June.

The second Supreme Court filing on Thursday concerned a subpoena from the Manhattan district attorney, Cyrus R. Vance Jr., a Democrat, for eight years of Mr. Trump’s personal and business tax returns.

The subpoena sought information concerning the reimbursements made to the president’s former lawyer, Michael D. Cohen, for payments to the pornographic film actress Stormy Daniels, who said she had an affair with Mr. Trump. The president has denied the relationship.

A unanimous three-judge panel of the United States Court of Appeals for the Second Circuit, in Manhattan, ruled this month against Mr. Trump. The court, in a focused ruling, said state prosecutors may require third parties to turn over a sitting president’s financial records for use in a grand jury investigation.

The New York case is further along at the Supreme Court, and involves more ambitious legal arguments. Mr. Trump’s lawyers, in a petition seeking review of the United States Court of Appeals for the Second Circuit’s decision, said he is immune from criminal investigation while he remains in office.

Even if some federal investigations may be proper, the petition went on, the Supreme Court should rule that state and local prosecutors may not seek information about a sitting president’s conduct.

“That the Constitution would empower thousands of state and local prosecutors to embroil the president in criminal proceedings is unimaginable,” Mr. Trump’s lawyers wrote.

In a brief urging the justices to deny review, Mr. Vance said the appeals court’s ruling was narrow and “plainly correct.” He added that it should make no difference that the subpoena came from state rather than federal authorities.

“If anything,” he wrote, “ordinary principles of federalism make this an easier case.”

Mr. Vance noted that the Supreme Court unanimously rejected claims of immunity in cases involving President Richard M. Nixon in United States v. Nixon in 1974 and President Bill Clinton in Clinton v. Jones in 1997.

Mr. Trump tweeted about the New York case Thursday morning. “Now the Witch Hunt continues with local New York Democrat prosecutors going over every financial deal I have ever done,” he wrote. “This has never happened to a President before. What they are doing is not legal. But I’m clean, and when I release my financial statement (my decision) sometime prior to Election, it will only show one thing — that I am much richer than people even thought.”

The Supreme Court could announce whether it will hear the New York case, Trump v. Vance, No. 19-635, in the coming weeks. If it does, its ruling would probably land in June in the final months of the presidential campaign.