The Republican memo, which was made available to all members of the House, is said to contend that officials from the two agencies were not forthcoming to a Foreign Intelligence Surveillance Court judge. Republicans accuse the agencies of not properly disclosing that the Democratic National Committee and Hillary Clinton’s 2016 presidential campaign helped finance research that was used to obtain a warrant for surveillance of Carter Page, a Trump campaign adviser. The research presented to the judge was assembled by a former British intelligence officer, Christopher Steele.

The memo is not limited to actions taken by the Obama administration, though. The New York Times reported on Sunday that the memo reveals that Deputy Attorney General Rod J. Rosenstein, a top Trump appointee, signed off an application to extend the surveillance of Mr. Page shortly after taking office last spring. The renewal shows that the Justice Department under Mr. Trump saw reason to believe that Mr. Page was acting as a Russian agent.

The inclusion of Mr. Rosenstein’s action in the memo could expose him to a torrent of criticism from Republicans on Capitol Hill and from conservatives in the news media who have seized on the surveillance to argue that the Russia investigation may have been tainted from the start. Mr. Rosenstein is overseeing that investigation because Attorney General Jeff Sessions recused himself. It was Mr. Rosenstein who appointed Robert S. Mueller III as special counsel.

Mr. Page, a former Moscow-based investment banker who went on to found a New York investment company, was on the F.B.I.’s radar for years. A trip he took to Russia in July 2016 while working for Mr. Trump’s campaign caught the bureau’s attention again, and by the fall of 2016, shortly after he left the campaign, American law enforcement officials began conducting surveillance on him.

To obtain the surveillance warrant, the government would have had to demonstrate probable cause that he was acting as an agent of Russia. Investigators must seek approval from the Justice Department for such a warrant, and then prosecutors take it to a surveillance court judge.

People familiar with the underlying application have portrayed the Republican memo as misleading in part, they say, because Mr. Steele’s information was insufficient to meet the standard for a FISA warrant. They said the application drew on other intelligence material that the Republican memo selectively omits. That other information remains highly sensitive, and releasing it would risk burning other sources and methods of intelligence-gathering about Russia.