A lawyer for House Democrats had argued to the court that the full evidentiary record assembled by Mr. Mueller is important, for example, in part because of suspicions that Mr. Trump may have lied under oath in his written answers to Mr. Mueller when he denied knowing about outreach to WikiLeaks regarding the contents of the emails that Russian hackers had stolen from Democrats, and the organization’s plans to publish them.

The appeals panel’s decision came less than two weeks after a different three-judge panel on the appeals court ruled, 2 to 1, that Congress had no right to sue to enforce a subpoena against an executive branch official who defied it — in that case, Donald F. McGahn II, the former White House counsel and a key witness to several efforts by Mr. Trump to obstruct the Russia investigation that were detailed in the Mueller report.

Judge Rogers and Judge Griffith were also part of the panel that heard the McGahn subpoena dispute but disagreed with each other. Over Judge Rogers’s dissent, Judge Griffith and another judge sided with the Trump administration in rejecting the House’s right to sue to enforce a subpoena for executive-branch information.

In the Mueller case, Judge Neomi Rao, a former administration official whom President Trump appointed to the appeals court last year, filed a dissenting opinion.

She argued that the grand-jury information dispute should turn out the same way as the McGahn subpoena case had turned out — with a decision that the House lacked standing to sue, delivering a victory for Mr. Trump’s secrecy powers — in part because the grand-jury records are currently in the control of the executive brach.

But in a concurring opinion, Judge Griffith said that the grand jury information was different because courts traditionally oversee grand juries and so the executive branch does not own the records, even if it is housing them. He also noted that there is a tradition of grand jury evidence being turned over to Congress for the impeachment of various officials.

“Federal courts, including courts in our own circuit, have approved the disclosure of grand jury materials to the House of Representatives in seven prior impeachment proceedings,” he wrote. “Congressional applications for access to grand jury materials have thus traditionally been thought capable of (and indeed to require) judicial resolution.”