Top congressional Republicans are shooting down talk of inviting a Russian delegation to the Capitol, even as GOP Sen. Rand Paul Randal (Rand) Howard PaulThe Hill's Morning Report - Sponsored by Facebook - Trump previews SCOTUS nominee as 'totally brilliant' Rand Paul says he can't judge 'guilt or innocence' in Breonna Taylor case Overnight Health Care: Health officials tell public to trust in science | Despair at CDC under Trump influence | A new vaccine phase 3 trial starts MORE (Ky.) pitched the idea during his trip to Moscow this week.

Senate Majority Leader Mitch McConnell Addison (Mitch) Mitchell McConnellTrump 'no longer angry' at Romney because of Supreme Court stance On The Money: Anxious Democrats push for vote on COVID-19 aid | Pelosi, Mnuchin ready to restart talks | Weekly jobless claims increase | Senate treads close to shutdown deadline The Hill's Campaign Report: Trump faces backlash after not committing to peaceful transition of power MORE (R-Ky.) and House Speaker Paul Ryan Paul Davis RyanKenosha will be a good bellwether in 2020 At indoor rally, Pence says election runs through Wisconsin Juan Williams: Breaking down the debates MORE (R-Wis.) have neither issued an invitation for a delegation from the Russian legislature nor are discussing it, spokesmen for the top GOP leaders told The Hill.

"Not anything we’ve discussed," said Brendan Buck, a spokesman for Ryan.

Asked if the Senate GOP leader had issued an invitation or was talking about it, McConnell spokesman David Popp added that "the short answer ... is no."

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The McConnell spokesman directed further questions to Paul's office, which didn't immediately respond to a request for comment on details of the Kentucky senator's invitation.

The pushback from GOP congressional leaders on hosting a group of their Russian counterparts comes after Paul raised the issue as part of his headline-grabbing trip this week to Moscow.

The Kentucky Republican said in a statement after a meeting with Konstantin Kosachev, the chairman of the Russian Federation Council committee on foreign affairs, that he had "invited the Russian Federation to send a delegation to the Capitol, and they have agreed to take this important next step."

Kosachev indicated that Moscow would be interested in organizing a meeting between members of the Russian legislature and their U.S. counterparts.

"The issue at hand is trying, perhaps, to organize a new meeting, this time at the level of the Senate Committee on Foreign Relations and the Federation Council’s Foreign Affairs Committee during the autumn session, that is, before the end of this year," he told Russian state media.

The Foreign Relations Committee, of which Paul is a member, is overseen by Sen. Bob Corker Robert (Bob) Phillips CorkerHas Congress captured Russia policy? Tennessee primary battle turns nasty for Republicans Cheney clashes with Trump MORE (R-Tenn.), who helped craft new Russia sanctions last year and is currently discussing the potential for further penalties.

"No invitation has been extended from the Senate Foreign Relations Committee," Micah Johnson, Corker's communications director, said in a statement on Thursday.

The distance between Paul and members of GOP leadership comes as the libertarian-minded senator has emerged as one of Trump's most vocal defenders on Russia.

Paul voted against new sanctions last year and blocked a resolution last month from Sen. Bernie Sanders Bernie SandersThe Hill's Campaign Report: Trump faces backlash after not committing to peaceful transition of power Bernie Sanders: 'This is an election between Donald Trump and democracy' The Hill's 12:30 Report: Trump stokes fears over November election outcome MORE (I-Vt.) to voice support for the intelligence community's findings that Russia meddled in the 2016 presidential election and back Trump sitting down with special counsel Robert Mueller Robert (Bob) MuellerCNN's Toobin warns McCabe is in 'perilous condition' with emboldened Trump CNN anchor rips Trump over Stone while evoking Clinton-Lynch tarmac meeting The Hill's 12:30 Report: New Hampshire fallout MORE.

"We should stand firm and say, 'Stay the hell out of our elections,' but we should not stick our head in the ground and say we're not going to talk to them," Paul said from the Senate floor.

Paul's defense of Trump comes as the president's warmer rhetoric toward Moscow — including remarks last month during a joint press conference with Russian President Vladimir Putin in Helsinki casting doubt on Russia's interference in the 2016 election — has raised eyebrows in Washington.

Both McConnell and Ryan previously said they would not issue an invitation for Putin to visit the Capitol even as the administration worked to orchestrate a meeting between Trump and his Russian counterpart in Washington, D.C.

Lawmakers on Capitol Hill are also becoming increasingly concerned that the Kremlin is working to interfere in the 2018 midterm elections.

Sen. Claire McCaskill Claire Conner McCaskillMomentum growing among Republicans for Supreme Court vote before Election Day Democratic-linked group runs ads in Kansas GOP Senate primary Trump mocked for low attendance at rally MORE (Mo.), one of the most vulnerable Democratic incumbents up for reelection this year, said late last month that Russian intelligence agents had targeted her staff with an attempted breach ahead of the November midterms.

While a group of GOP senators traveled to Russia last month, Paul's trip to Moscow — and him touting that he delivered a letter from Trump to Putin — has drawn questions.

"This is weird. I wonder how Ambassador [Jon] Huntsman feels about it? And separation of powers between executive and legislative branches is a good thing. Let senators be senators and ambassadors be ambassadors," former Ambassador Michael McFaul said in a tweet about Paul delivering the letter.

The White House later clarified that the letter was an introduction for Paul to Putin, adding that it was requested by the GOP senator.

Paul has defended his trip, and his rhetoric, arguing it's important to keep a dialogue open between the United States and Russia despite the sour state of relations.

Doug Stafford, an adviser for Paul, told the Louisville Courier-Journal that the senator was acting in his capacity as a member of the Foreign Relations Committee "and in cooperation with President Trump Donald John TrumpSteele Dossier sub-source was subject of FBI counterintelligence probe Pelosi slams Trump executive order on pre-existing conditions: It 'isn't worth the paper it's signed on' Trump 'no longer angry' at Romney because of Supreme Court stance MORE and the State Department."

"Other senators ... may join in efforts for dialogue, diplomacy, and peace if they see fit," Stafford added in the statement to the Kentucky newspaper. "Senator Paul didn’t need anyone’s permission to extend this invite."