Mr. Trump’s congressional allies reacted angrily to the revelation of Mr. Halper’s role in the F.B.I. investigation, accusing the bureau of “spying” on the Trump campaign. The president himself has called the issue a “scandal” on Twitter.

“Reports are there was indeed at least one FBI representative implanted, for political purposes, into my campaign for president,” he wrote in May.

“If true — all time biggest political scandal!”

Congressional leaders have received two briefings about Mr. Halper’s role in the F.B.I. investigation. One of the briefings was attended by John F. Kelly, the White House chief of staff, and Emmet T. Flood, a White House lawyer handling issues related to the special counsel’s Russia investigation — leading to vocal criticism on Capitol Hill that it was improper for White House officials to attend a classified briefing about an investigation that involves the president.

Representative Devin Nunes of California, the chairman of the House Intelligence Committee and one of the president’s staunchest defenders in Congress, for weeks has demanded that the full House and Senate Intelligence Committees be given access to documents about the informant’s role in the campaign. He has accused the Justice Department of “obstruction” of a congressional investigation.

Democrats have argued that the true aim of the Republicans is to undermine the Russia investigation — which in May 2017 was taken over by the special counsel, Robert S. Mueller III — and that Republicans want access to F.B.I. files to gain information they can use against the inquiry.

Intelligence and law enforcement officials — including Dan Coats, the director of national intelligence, and Christopher A. Wray, the F.B.I. director — were opposed to expanding the number of lawmakers who can read the classified files, according to people with knowledge of their thinking.

In a letter to Mr. Coats on Thursday, Democratic members of the Gang of Eight protested the release of the documents, saying that it “contravenes your representation to us and our colleagues that this information would not be shared outside that group.”