WASHINGTON — Top Democrats in the House and the Senate demanded on Tuesday that Republican leaders stifle conservative attacks on the special counsel’s Russia investigation and compel President Trump’s senior national security advisers to testify to Congress about Monday’s extraordinary summit meeting with President Vladimir V. Putin of Russia.
“Words are not enough,” Senator Chuck Schumer of New York, the Democratic leader, said in blistering remarks on the Senate floor. “Our response to the debasement of American interest before an adversary demands a response not just in words but in deeds.”
Republicans from across the ideological spectrum were left reeling on Monday after Mr. Trump stood beside Mr. Putin and, in a spectacular display for an American president, sided with the Russian leader over his own government’s assessment of Russian election interference in 2016. Most said plainly that they did not agree, but they made no immediate proposals to check Mr. Trump beyond statements.
Republican leaders instead advanced cautiously on Tuesday. Early in the day, they appeared to coalesce around the idea of possibly enacting additional sanctions to punish Russia for its interference campaign.
“Here is what we have already done and here is what we could continue to do, which is put sanctions on Russia,” Speaker Paul D. Ryan of Wisconsin told reporters at a news conference.
Mr. Ryan stepped around criticizing Mr. Trump head on, saying instead that he had no doubt that Russians meddled in the election and that Mr. Putin should be viewed warily. He said that the relevant House committees should determine if additional sanctions were necessary.
The idea got a nod of approval in the Senate from John Cornyn of Texas, the No. 2 Senate Republican. Senator Mitch McConnell of Kentucky, the majority leader, did not mention United States-Russia relations in his opening remarks on Tuesday.
“We ought to look at perhaps some additional sanctions,” Mr. Cornyn said in an interview. “As opposed to just a messaging exercise, I think we ought to tighten the screws on Russia.”
Senator Bob Corker of Tennessee, one of Mr. Trump’s leading Republican critics from his perch as chairman of the Senate Foreign Relations Committee, signaled optimism that the Helsinki meeting might finally push Congress to reassert its authority as a coequal branch of government.
“You see people down on the floor scurrying around trying to find a way to push back against what has happened,” Mr. Corker said. “The dam has broken. What we’ve got to figure out is how do we deal with it, because the president in 15 minutes can foul up six months or a year of good will.”
Mr. Corker said he expected Secretary of State Mike Pompeo to testify before his committee next week. He called for a vote on legislation intended to give Congress a say on another foreign policy matter deeply dividing Republicans, the president’s implementation of national security tariffs. And he said that he was in discussions with Senator Marco Rubio, Republican of Florida, to try to advance a bill written with Senator Chris Van Hollen, Democrat of Maryland, that would create new sanctions authorities to punish Russia should it interfere this November.
Democrats were not impressed. Representative Nancy Pelosi of California, the minority leader in the House, indicated to fellow Democrats that she did not intend to wait for Republicans and would try to force their hand on the House floor.
“House Republicans are engaged in a stunning abdication of leadership: cravenly refusing to take any action to secure our elections from foreign attack, and instead offering only weak words while bringing to the floor an appropriations package that eliminates funding for states to protect their election systems,” she wrote in a letter to Democrats.
Ms. Pelosi said that the party would try to force a vote on a resolution condemning Mr. Trump’s remarks in Helsinki and affirming the findings of American intelligence agencies that Mr. Putin ordered an influence campaign meant to tip the scales in 2016. Democrats would also try to force a vote to increase funding for states to enhance the security of their voting systems, she said.
In addition to calling for a hearing with Mr. Pompeo and other national security advisers, Mr. Schumer put his weight behind strengthening sanctions. He called on Mr. Trump to demand the extradition of 12 Russian intelligence officers indicted on Friday for cyberattacks in the run-up to the 2016 election. And he urged Republican leaders to immediately move to consider legislation devised to bolster election security.
“These are five simple things we could do together, Democrat and Republican,” he said.
The comments appeared to have little effect, at least on Mr. Trump’s outward stance. Back in Washington, he lauded the summit meeting as a success and publicly thanked Senator Rand Paul of Kentucky, one of the few Republican voices who came to his defense on Monday.
On Tuesday, though, the president picked up more defenders, as members of the House Freedom Caucus used a “Conversation With Conservatives” forum to heap praise on Mr. Trump for meeting with Mr. Putin, accuse his critics of undermining him and blame reporters for asking questions that Representative Andy Biggs, Republican of Arizona, described as “really odd” and “a little bit unsettling.”
John O. Brennan, the former C.I.A. director who on Monday suggested Mr. Trump’s behavior had been treasonous, came in for particular scorn. “If there’s anything treasonous that’s gone on,” said Representative Warren Davidson of Ohio, “it’s that operation right now to sow distrust in our duly elected president of the United States.”