WASHINGTON — President Trump over the summer repeatedly urged senior Senate Republicans, including the chairman of the Senate Intelligence Committee, to end the panel’s investigation into Russia’s interference in the 2016 election, according to a half dozen lawmakers and aides. Mr. Trump’s requests were a highly unusual intervention from a president into a legislative inquiry involving his family and close aides.
Senator Richard Burr of North Carolina, the intelligence committee chairman, said in an interview this week that Mr. Trump told him that he was eager to see an investigation that has overshadowed much of the first year of his presidency come to an end.
“It was something along the lines of, ‘I hope you can conclude this as quickly as possible,’” Mr. Burr said. He said he replied to Mr. Trump that “when we have exhausted everybody we need to talk to, we will finish.”
In addition, according to lawmakers and aides, Mr. Trump told Senator Mitch McConnell of Kentucky, the Republican leader, and Senator Roy Blunt, Republican of Missouri and a member of the intelligence committee, to end the investigation swiftly.
Senator Dianne Feinstein, a California Democrat who is a former chairwoman of the intelligence committee, said in an interview this week that Mr. Trump’s requests were “inappropriate” and represented a breach of the separation of powers.
“It is pressure that should never be brought to bear by an official when the legislative branch is in the process of an investigation,” Ms. Feinstein said.
Raj Shah, a White House spokesman, said on Thursday that the president had not acted improperly. Mr. Trump, he said, “at no point has attempted to apply undue influence on committee members’’ and believes “there is no evidence of collusion and these investigations must come to a fair and appropriate completion.’’
Mr. Trump’s requests of lawmakers to end the Senate investigation came during a period in the summer when the president was particularly consumed with Russia and openly raging at his own attorney general, Jeff Sessions, for recusing himself from any inquiries into Russian meddling in the election. Mr. Trump often vented to his own aides and even declared his innocence to virtual strangers he came across on his New Jersey golf course.
In this same period, the president complained frequently to Mr. McConnell about not doing enough to bring the investigation to an end, a Republican official close to the leader said.
Republicans played down Mr. Trump’s appeals, describing them as the actions of a political newcomer unfamiliar with what is appropriate presidential conduct.
Mr. Burr said he did not feel pressured by the president’s appeal, portraying it as the action of someone who has “never been in government.” But he acknowledged other members of his committee have had similar discussions with Mr. Trump. “Everybody has promptly shared any conversations that they’ve had,” Mr. Burr said.
One of them was Mr. Blunt, who was flying on Air Force One with Mr. Trump to Springfield, Mo., in August when he found himself being lobbied by the president “to wrap up this investigation,” according to a Republican official familiar with the conversation.
Mr. Blunt was not bothered by Mr. Trump’s comments, the official said, because he did not see them bearing a “sinister motive.’’
But Mr. Burr and Mr. Blunt have both taken steps to limit their interaction with Mr. Trump this year, not wanting to create the perception of coziness as they conduct a highly sensitive investigation into contacts between the president’s campaign and Moscow last year.
Robert S. Mueller III, the Justice Department’s special counsel who is leading a separate investigation into Russian meddling in the 2016 election, is also examining whether Mr. Trump tried to obstruct justice when he fired James B. Comey, the F.B.I. director who was running a federal inquiry into the matter.
Mr. Trump also called other lawmakers over the summer with requests that they push Mr. Burr to finish the inquiry, according to a Republican senator who requested anonymity to discuss his contact with the president.
This senator, who was alarmed upon hearing word of the president’s pleas, said Mr. Trump’s request to the other senators was clear: They should urge Mr. Burr to bring the Russia investigation to a close. The senator declined to reveal which colleagues Mr. Trump had contacted with the request.
Some of Mr. Trump’s advisers feared he would move to fire Mr. Mueller, an option that the president pointedly left open in an Oval Office interview with The New York Times in July.
During this time, Mr. Trump made several calls to senators without senior staff present, according to one West Wing official. According to senators and other Republicans familiar with the conversations, Mr. Trump would begin the talks on a different topic but eventually drift toward the Russia investigation.
In conversations with Mr. McConnell and Senator Bob Corker, the Tennessee Republican who is chairman of the Senate Foreign Relations Committee, Mr. Trump voiced sharp anger that congressional Republicans were not helping lift the cloud of suspicion over Russia, the senators told political allies. The Times reported in August that the president had complained to Mr. McConnell that he was failing to shield Mr. Trump from an ongoing Senate inquiry.
The earlier call with Mr. Burr, however, was perhaps the most invasive, given Mr. Burr’s role directly supervising the Senate’s investigation of Mr. Trump.
Mr. Burr told other senators that Mr. Trump had stressed that it was time to “move on” from the Russia issue, using that language repeatedly, according to people who spoke with Mr. Burr over the summer. One Republican close to Mr. Burr, who spoke on condition of anonymity, said that Mr. Trump had been “very forceful.”
Asked why Mr. Trump is so irritated with the investigation, Mr. Burr said: “In his world it hampers his ability to project the strength he needs to convey on foreign policy.”
Mr. Burr said Mr. Trump was not fully aware of the impropriety of his request because the president still has the mind-set of a businessman rather than a politician. “Businessmen are paid to skip things that they think they can skip and get away with,” he said.
This past summer, Mr. Trump also contacted Senator Thom Tillis, a North Carolina Republican who in August introduced a bipartisan bill limiting the president’s power to dismiss special prosecutors — a measure widely seen as aimed at protecting Mr. Mueller from Mr. Trump. In an interview this week, Mr. Tillis said the president “just asked me where my head was” on the legislation and described the exchange as “pleasant.” Mr. Trump did not press him on the Senate investigation, said Mr. Tillis, who is not on the intelligence committee.
Republicans said Mr. Trump’s ire often went beyond the intelligence committee investigation and spilled over a range of issues that touched on Russia and his relationship with Congress.
Another Republican senator said Mr. Trump had not urged him to help bring the Russia inquiry to a halt. Instead, the senator said, the president nudged him to begin an investigation into Hillary Clinton’s connection with the intelligence-gathering firm Fusion GPS, which produced a dossier of allegations about Mr. Trump’s ties to Moscow.
Mr. McConnell — who over the summer was quickly notified of Mr. Trump’s calls to his Senate colleagues — told multiple associates that Mr. Trump appeared unable to distinguish traditional policy concerns about Russia from more specific questions about Russian interference in the presidential race.
The Senate leader told associates that Mr. Trump did not seem to recognize that the Republican Party traditionally took a suspicious view of Russia, or that lawmakers could favor punishing Russia without questioning Mr. Trump’s victory in 2016. The president had reluctantly signed a bill imposing sanctions on Moscow on Aug. 2, using an extraordinary written statement to lash out against what he viewed as a usurping of executive authority from a Congress that “could not even negotiate a health care bill after seven years of talking.”
Mr. Trump, Mr. McConnell told associates, appeared inclined to treat criticism of Russian meddling in the United States as giving credence to unproven allegations that his campaign colluded with foreign actors.
In that respect, Mr. Trump’s private consternation mirrored some of his public complaints about the Russia issue. He has continued to seethe regularly, and openly, about the scrutiny of Russia’s political activities, tweeting just last weekend: “Since the first day I took office, all you hear is the phony Democrat excuse for losing the election, Russia, Russia, Russia.”