Washington(CNN) On the fourth chaotic day of fallout from President Donald Trump's hugely consequential remarks regarding the US relationship to Russia, Congress did something rare: it took unified action.

The Senate overwhelmingly approved a proposal to oppose sending US officials to be interrogated by Russian officials, though it's unclear what if any concrete legislative options Republican leaders in Congress would take beyond statements and non-binding resolutions.

The 98-0 vote came after the White House announced it now disagreed with the proposal from Russian President Vladimir Putin to question former US ambassador to Russia Michael McFaul and others, which the White House had up until Thursday afternoon said it was considering.

Thursday's vote was a rare sign of consensus to address the divisive fallout of Trump's highly controversial remarks earlier this week, where the US President appeared to back Putin over the US intelligence community assessment that Russia interfered with the 2016 US presidential election. Trump's comments have reverberated across Capitol Hill all week as lawmakers from both parties sharply criticized the President, and Republicans in Congress -- who control both chambers -- are considering multiple options for how to respond.

Senate Majority Leader Mitch McConnell also announced plans for hearings on a sanctions bill from Florida Republican Sen. Marco Rubio and Maryland Democratic Sen. Chris Van Hollen. The sanctions would snap into place if the director of national intelligence identified additional Russian meddling into future elections.

But lawmakers -- or even just Republicans -- are far from unified on other options. The 98-0 vote followed another one earlier Thursday, where a top Senate Republican leader blocked passage of a nonbinding bipartisan resolution -- proposed by another Republican senator -- backing the US intelligence community.

Republicans criticize proposal to send ex-ambassador back to Russia

The resolution that passed Thursday expressed the sense of the Senate that no current or former diplomat, civil servant, law enforcement official, member of the armed forces or political appointee should be made available to Putin's government for an interrogation. The proposal was produced by Senate Minority Leader Chuck Schumer, a New York Democrat.

Earlier Thursday, Republican senators criticized the White House for temporarily entertaining a proposal raised by Putin to interrogate Americans in exchange for assistance in the ongoing US investigation into election interference. The White House later said it did not support the proposal.

"It is a proposal that was made in sincerity by President Putin, but President Trump disagrees with it," press secretary Sarah Sanders said in a statement Thursday. "Hopefully President Putin will have the 12 identified Russians come to the United States to prove their innocence or guilt."

The Americans wanted for questioning by Moscow include Michael McFaul, the former US ambassador to Russia, and American-born financier Bill Browder, who successfully lobbied the US government to impose new sanctions on Moscow.

Before the White House released the statement, Sen. Bob Corker, a Tennessee Republican and chairman of the Senate Foreign Relations Committee, wouldn't elaborate to CNN but called the idea of sending Americans to be interrogated by Russians "bad."

"I have no idea why that's even coming into consciousness," he said.

And Sen. Johnny Isakson, a member of the Senate Foreign Relations Committee, also slammed the idea.

"I don't think we ought to be sending anyone back Russia to be interviewed by the Russians," Isakson, the Georgia Republican, told CNN. "I don't think we should do that."

Votes blocked earlier Thursday

Sen. John Cornyn, a GOP Texan and the second-ranking Republican in the chamber, complained the first resolution was "purely a symbolic act" and said he wanted Senate committees to dig into the issues involved before deciding next steps. Cornyn said those steps could include new sanctions against Russia to punish that country for its interference in US elections, something Cornyn said he supports.

The resolution Cornyn blocked was authored by Sen. Jeff Flake, an Arizona Republican, and Sen. Chris Coons, a Delaware Democrat. Both are prominent Trump critics.

Their proposal rejects Putin's denial of election interference, calls for the immediate enactment of sanctions passed by Congress last year and asks Senate committees to hold hearings into what exactly happened in the private meeting between Putin and Trump, including obtaining relevant notes and other information.

Key Republican senator: Seeking Trump translator's notes 'not appropriate'

Cornyn noted that Secretary of State Mike Pompeo is scheduled to appear before the Senate Foreign Relations Committee next week and that Senate Majority Leader Mitch McConnell has asked that committee, as well as the Senate Banking Committee, to hold hearings soon on the implementation of legislation that Congress passed last year imposing sanctions on Russia over the election interference issue.

Flake said from the floor that "empirical, objective truth has taken a beating over the past 18 months."

"As we saw in Helsinki on Monday, entertaining the untruths of a dictator has the same effect," Flake continued. "Passing this resolution will let our constituents, the administration, our allies and our adversaries know that here in the Senate, we do not entertain the deceit of dictators."

Cornyn defended Trump, saying the President agrees Russia interfered despite what he said at the news conference with Putin.

"I agree in Helsinki he was less than clear about that, but he came back and said he's misspoke and reaffirmed his earlier position that, yes, the Russian government had interfered in the election," Cornyn said.

The moves came on the same day a new CBS poll found 68% of Republicans support Trump's actions in Helsinki, more evidence for GOP senators that they may anger their base voters if they move too strongly against the President.

Also Thursday, Sen. Rand Paul, a Kentucky Republican, objected to a different resolution from Sen. Bernie Sanders, a Vermont independent who caucuses with Democrats, that among other things says the Senate accepts the intelligence community's findings that Russia interfered in the 2016 elections and takes steps to safeguard special counsel Robert Mueller, who is investigating that and other issues.

Paul argued Trump's critics are wrong to oppose him trying to work with Putin and Russia.

CORRECTION: This story has been updated to correct McFaul's former title.