“We cannot allow foreign governments to interfere in our democracy,” Representative Michael McCaul, a Texas Republican who is the chairman of the Homeland Security Committee and was considered by Mr. Trump for secretary of Homeland Security, said at the conservative Heritage Foundation. “When they do, we must respond forcefully, publicly and decisively.”

He has promised hearings, saying the Russian activity was “a call to action,” as has Senator John McCain, one of the few senators left from the Cold War era, when the Republican Party made opposition to the Soviet Union — and later deep suspicion of Russia — the centerpiece of its foreign policy.

Even one of Mr. Trump’s most enthusiastic supporters, Representative Devin Nunes, a California Republican, said on Friday that he had no doubt about Russia’s culpability. His complaint was with the intelligence agencies, which he said had “repeatedly” failed “to anticipate Putin’s hostile actions,” and with the Obama administration’s lack of a punitive response.

Mr. Nunes, the chairman of the House Intelligence Committee, said that the intelligence agencies had “ignored pleas by numerous Intelligence Committee members to take more forceful action against the Kremlin’s aggression.” He added that the Obama administration had “suddenly awoken to the threat.”