Mr. Trump has long been mistrustful of Mr. Rosenstein, the Justice Department’s No. 2 official, who appointed the special counsel, Robert S. Mueller III, and now oversees his investigation into Mr. Trump’s campaign and possible obstruction of justice by the president. Mr. Trump considered firing Mr. Rosenstein last summer. Instead, he ordered Mr. Mueller to be fired, then backed down after the White House counsel refused to carry out the order, The New York Times reported last week.
Mr. Trump is now again telling associates that he is frustrated with Mr. Rosenstein, according to one official familiar with the conversations.
It is difficult to judge whether Republicans’ criticism of the surveillance has merit. Although House members have been allowed to view the Republican memo in a secure setting, both that memo and a Democratic one in rebuttal remain shrouded in secrecy. And the applications to obtain and renew the warrant from the Foreign Intelligence Surveillance Court are even more closely held. Only a small handful of members of Congress and staff members have reviewed them.
Republicans on the House Intelligence Committee, whose staff wrote the memo, could vote as early as Monday, using an obscure House rule, to effectively declassify its contents and make it available to the public. Mr. Trump would have five days to try to block their effort, potentially setting up a high-stakes standoff between the president and his Justice Department, which opposes its immediate release.
The White House has made clear to the Justice Department in recent days that it wants the Republican memo to be made public. Asked about the issue on CBS’s “Face the Nation” on Sunday, Marc Short, the White House’s head of legislative affairs, said that if the memo outlined serious concerns, “the American people should know that.”
But Stephen E. Boyd, an assistant attorney general, warned in a letter last week to the committee’s chairman, Representative Devin Nunes of California, that it would be “extraordinarily reckless” to release a memo drawing on classified information without official review and pleaded with the committee to consult the Justice Department. He said the department was “unaware of any wrongdoing related to the FISA process.”
To obtain the warrant involving Mr. Page, the government needed to show probable cause that he was acting as an agent of Russia. Once investigators get approval from the Justice Department for a warrant, prosecutors take it to a surveillance court judge, who decides whether to approve it.
A Justice Department spokeswoman declined to comment, and a spokesman for Mr. Nunes did not reply to requests for comment. The people familiar with the contents of the memo spoke on the condition of anonymity because the details remained secret.
A White House spokesman, Hogan Gidley, said in a statement: “The president has been clear publicly and privately that he wants absolute transparency throughout this process. Based on numerous news reports, top officials at the F.B.I. have engaged in conduct that shows bias against President Trump and bias for Hillary Clinton. While President Trump has the utmost respect and support for the rank-and-file members of the F.B.I., the anti-Trump bias at the top levels that appear to have existed is troubling.”
Mr. Page, a former Moscow-based investment banker who later founded an investment company in New York, had been on the F.B.I.’s radar for years. In 2013, an investigation revealed that a Russian spy had tried to recruit him. Mr. Page was never charged with any wrongdoing, and he denied that he would ever have cooperated with Russian intelligence officials.
But a trip Mr. Page took to Russia in July 2016 while working on Mr. Trump’s campaign caught the bureau’s attention again, and American law enforcement officials began conducting surveillance on him in the fall of 2016, shortly after he left the campaign. It is unclear what they learned about Mr. Page between then and when they sought the order’s renewal roughly six months later. It is also unknown whether the surveillance court granted the extension.
The renewal effort came in the late spring, sometime after the Senate confirmed Mr. Rosenstein as the Justice Department’s No. 2 official in late April. Around that time, following Mr. Trump’s firing of James B. Comey as F.B.I. director in May, Mr. Rosenstein appointed Mr. Mueller, a former head of the bureau, to take over the department’s Russia investigation. Mr. Rosenstein is overseeing the inquiry because Attorney General Jeff Sessions has recused himself.
Sean Hannity, the Fox News host, who is close to Mr. Trump and House Republicans, signaled interest in Mr. Rosenstein this month as news of the memo’s existence first circulated, asking on air if Mr. Rosenstein had played a role in extending the surveillance. “I’m very interested about Rod Rosenstein in all of this,” he said.
In a speech on Friday in Norfolk, Va., Mr. Sessions appeared to wade into the debate. Without mentioning the Republican memo, he said that federal investigations must be free of bias, and that he would not condone “a culture of defensiveness.” While unfair criticism should be rebutted, he added, “it can never be that this department conceals errors when they occur.”
