The new petition stressed the novelty and importance of the second dispute.

“This is a case of firsts,” Mr. Trump’s petition said. “It is the first time that Congress has subpoenaed personal records of a sitting president. It is the first time that Congress has issued a subpoena, under the guise of its legislative powers, to investigate the president for illegal conduct. And, it is the first time a court has upheld any congressional subpoena for any sitting president’s records of any kind.”

The Supreme Court has agreed to hear earlier cases, the petition said, when “the president has been subjected to novel legal process and seeks review.” In cases involving Presidents Richard M. Nixon and Bill Clinton, United States v. Nixon in 1974 and Clinton v. Jones in 1997, the court granted review but in the end handed both presidents unanimous losses.

The Nixon case led to his resignation in the face of mounting calls for his impeachment. The Clinton case led to Mr. Clinton’s impeachment, though he survived a Senate vote on his removal.

The new case concerns a subpoena that the House Oversight and Reform Committee issued in April after it learned that Mr. Trump’s ethics disclosure forms did not list a debt for hush-money payments made in the run-up to the 2016 election. Mr. Trump and his company reimbursed 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. (Mr. Cohen is serving a three-year sentence in prison related to the case.)

Mr. Cohen also told the committee that Mr. Trump had inflated and deflated descriptions of his assets on financial statements to obtain loans and reduce his taxes.