WASHINGTON — Top lawmakers, including the chairman of the Senate Intelligence Committee, demanded on Tuesday that the White House provide details concerning President Trump’s meeting last week with Russian officials during which he revealed sensitive intelligence information.
The Senate majority leader, Mitch McConnell, who has been largely silent on the president’s increasing troubles concerning Russia, carefully pleaded with the administration to stop impeding the Republican agenda. Even as he tried to change the conversation to health care, the focus remained firmly on the president and Russia.
“I think we could do with a little less drama from the White House on a lot of things so that we can focus on our agenda,” Mr. McConnell said in an interview on Bloomberg Television on Tuesday morning, reflecting an increasingly frustrated Republican majority over the White House mishaps.
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Later, during a news conference on Capitol Hill, when asked if he was concerned about Mr. Trump’s competence in handling intelligence information, Mr. McConnell paused for several beats before responding, “No.”
Lawmakers in both parties were largely confounded by the latest controversy, one in a series of self-made crises that has hobbled their ability to move forward with any of Mr. Trump’s policy priorities.
“Once again, we are faced with inexplicable stories coming from the White House that are highly troubling,” said Representative Barbara Comstock, Republican of Virginia, who is up for re-election next year in a highly competitive swing district.
“We need to have immediate classified briefings on what occurred at this meeting so that Congress can at least know as much as Russian leaders and know the impact on our national security, our allies, and our men and women protecting our country,” she said in a statement.
The often shifting narrative coming out of the White House has also made it nearly impossible for lawmakers to get a grasp of what happened and how to respond, or to weigh the potential damage to their party.
“In order for me to judge the appropriateness or not, I have to have context,” Senator Thom Tillis, Republican of North Carolina, said. “If it is in fact true that this information was shared with the Russian ambassador, it seems to me it’d be O.K. to be shared with U.S. senators.”
Because Mr. McConnell tends to refrain from criticizing the White House, his words, while muted, were almost certainly heard by other Republicans as a rebuke.
Yet Mr. McConnell did not go as far on Tuesday as Senator Susan Collins, Republican of Maine, a member of the Senate Intelligence Committee, who suggested in a statement that the information discussed by Mr. Trump with the Russians might have endangered allies. “The disclosure of highly classified information has the potential to jeopardize sources and to discourage our allies from sharing future information vital to our security,” Ms. Collins.
Senator Richard M. Burr of North Carolina, the chairman of the Intelligence Committee, has requested that the White House provide information to the committee on the incident and had yet to hear a reply on Tuesday.
Democrats, whose powers are limited — they have some subpoena powers if they are able to attract the support of at least one Republican on the Intelligence Committee — spent a great deal of Tuesday strongly criticizing Mr. Trump.
“We rely on our intelligence from our allies to keep us safe,” said Senator Chuck Schumer of New York, the Democratic leader, who took the Senate floor Tuesday morning to demand that the Intelligence Committee be given access to the transcripts of the meeting between Mr. Trump and the Russians. “If our allies abroad can’t trust us to keep sensitive information close to the vest, they may no longer share it with us.”
Over all, Republicans were tempered in their criticism of Mr. Trump, with many arguing that the president was acting within his authority to declassify information. But many expressed privately — and some publicly — that they would like the White House to function with far greater discipline.
“There’s some alignments that need to take place over there, and I think they’re fully aware of that,” said Senator Bob Corker, Republican of Tennessee and the chairman of the Foreign Relations Committee. “Just the decision-making processes and everybody being on the same page.”
Other Republicans seemed to give the White House the benefit of the doubt even as they called for more information.
“I suspect the administration will brief the Congress more fully on exactly what transpired,” Senator Tom Cotton, Republican of Arkansas and a former Army captain, said on Tuesday in an interview on Hugh Hewitt’s radio show.
“But I have much greater confidence in the word of H. R. McMaster on the record, in front of cameras, than I do anonymous sources in the media,” Mr. Cotton said, referring to Mr. Trump’s national security adviser.
Mike Pompeo, the director of the C.I.A., was expected to brief members of the House Intelligence Committee on Tuesday evening. Emily Hytha, a spokeswoman for Representative K. Michael Conaway of Texas, the Republican who is heading the House’s investigation into Russian meddling in last year’s presidential election, said the meeting had been scheduled “several weeks ago.”