The Supreme Court is expected to announce whether it will hear the appeals in the coming weeks. If it declines to step in, appeals court rulings requiring disclosure will stand, and Mazars has indicated that it will supply the requested records. If the Supreme Court agrees to hear the cases, it will probably hear arguments early next year and issue decisions by June.

No stay from the Supreme Court was needed in the Manhattan case because prosecutors there had agreed not to seek immediate release of the records in exchange for a prompt request for Supreme Court review. There was no such agreement in the House case.

“It has now been seven months since the Oversight Committee asked for these records,” Representative Carolyn B. Maloney, a New York Democrat and the committee’s acting chairwoman, said in a statement last week. “It is time for the president to let us do our job and stop blocking Mazars from complying with the committee’s lawful subpoena.”

Both subpoenas sought information concerning 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.

The House subpoena also sought records prompted by Mr. Cohen’s testimony that Mr. Trump had inflated and deflated descriptions of his assets on financial statements to obtain loans and reduce his taxes.