But there still appeared to be little momentum for a select committee to investigate Russian interference — an idea that Senator Mitch McConnell of Kentucky, the majority leader, has long resisted.
Few Republicans in Congress lamented Mr. Flynn’s departure from the administration, crediting Mr. Trump for hastening his resignation, despite reports that White House officials knew for weeks that Mr. Flynn had misled colleagues.
“I think it’s pretty obvious why he decided to make the decision he did,” Mr. McConnell said of Mr. Trump.
At the same time, in a striking role reversal, the party long known for its universally hawkish stance toward Russia is now ceding some of that ground to Democrats.
On Tuesday, Democrats tried to make it clear that Mr. Flynn’s resignation must be only the first chapter in the story of Russia’s involvement in the 2016 election.
“The crisis here rises above party,” said the Democratic leader in the Senate, Senator Chuck Schumer of New York, calling for an “independent, nonpartisan” investigation and insisting that Jeff Sessions, the new attorney general who was active in Mr. Trump’s campaign alongside Mr. Flynn, recuse himself from any review.
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Mr. McCain, one of the most vocal critics of Mr. Trump’s approach and tenor toward Russia, was among the earliest to speak out forcefully on Tuesday.
“General Flynn’s resignation also raises further questions about the Trump administration’s intentions toward Vladimir Putin’s Russia, including statements by the president suggesting moral equivalence between the United States and Russia despite its invasion of Ukraine, annexation of Crimea, threats to our NATO allies, and attempted interference in American elections,” Mr. McCain said in a statement.
However, Mr. McCain did not restate his earlier calls for a select committee to investigate Russian interference in the presidential election, which has not been supported by Mr. McConnell, who said any such investigations should be the purview of the relevant Senate committees. Mr. McCain has vowed that his committee will conduct a thorough inquiry and that he had full confidence in Mr. Trump’s defense and homeland security secretaries, calling his partnership with them “excellent.”
Most Republicans pursued similar arguments, deflecting questions about the need for further investigations into the administration’s ties to Russia. But a handful expressed concern about the pace of progress.
“It is frustrating to understand how we’re going to get a full, in-depth look at all the things that have happened,” said Senator Bob Corker, Republican of Tennessee, chairman of the Foreign Relations Committee. “I think this episode does heighten the intensity around wanting to make sure that it’s fulsome and that we understand all aspects of what’s occurred.”
Senator Lindsey Graham, Republican of South Carolina, identified a possible silver lining.
“I just think it makes it almost impossible for them to lift sanctions now,” said Mr. Graham, who introduced bipartisan legislation last week that would require congressional approval for Mr. Trump to lift sanctions against Russia. “That’s sort of the good news.”
Mr. Graham suggested, gently, that Republicans should take care to avoid any appearance of hypocrisy.
“I think it’s important for us to be informed about the phone call. Did he do it by himself? Did he kind of go rogue or did somebody suggest to him to call the Russians?” he said. “I know we would be upset as Republicans if the Obama administration had done this.”