Senate Majority Leader Mitch McConnell Addison (Mitch) Mitchell McConnellDemocratic senator to party: 'A little message discipline wouldn't kill us' House to vote on resolution affirming peaceful transition of power Republican lawyers brush off Trump's election comments MORE (R-Ky.) is throwing his support behind a resolution condemning the House impeachment inquiry into President Trump Donald John TrumpFederal prosecutor speaks out, says Barr 'has brought shame' on Justice Dept. Former Pence aide: White House staffers discussed Trump refusing to leave office Progressive group buys domain name of Trump's No. 1 Supreme Court pick MORE.

Senate Republicans are expected to introduce a “Graham-McConnell” resolution later Thursday “condemning the House of Representatives closed door, illegitimate impeachment inquiry,” per a release from Sen. Lindsey Graham Lindsey Olin GrahamLincoln Project mocks Lindsey Graham's fundraising lag with Sarah McLachlan-themed video The Hill's Morning Report - Sponsored by Facebook - Republicans lawmakers rebuke Trump on election Trump dumbfounds GOP with latest unforced error MORE’s (R-S.C.) office.

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McConnell confirmed to reporters that he will back the measure, saying, "Obviously I support it."

Graham said earlier this week that he was planning to introduce the resolution, telling Fox News’s Sean Hannity Sean Patrick HannityFormer Florida attorney general calls Kyle Rittenhouse 'a little boy out there trying to protect his community' Sunday shows preview: Justice Ginsburg dies, sparking partisan battle over vacancy before election Cruz: Trump should nominate a Supreme Court justice next week MORE that it “puts the Senate on record condemning the House."

It’s unclear if the resolution will come up for a vote. It would allow GOP senators, who have grown increasingly frustrated with the House, to formalize their opposition. But it would also likely fail to get the 60 votes needed to pass.

McConnell and his caucus have increasingly railed against the House impeachment inquiry process, which includes near-daily closed-door depositions with current and former officials.

"Overturning the results of an American election requires the highest level of fairness and due process, as it strikes at the core of our democratic process," McConnell wrote in a tweet earlier this month.

"So far, the House has fallen far short by failing to follow the same basic procedures that it has followed for every other President in our history," he added.

Trump and his allies have pressed for House Democrats to hold a vote formally launching the impeachment inquiry, something Speaker Nancy Pelosi Nancy PelosiDemocratic senator to party: 'A little message discipline wouldn't kill us' Overnight Health Care: New wave of COVID-19 cases builds in US | Florida to lift all coronavirus restrictions on restaurants, bars | Trump stirs questions with 0 drug coupon plan Overnight Defense: Appeals court revives House lawsuit against military funding for border wall | Dems push for limits on transferring military gear to police | Lawmakers ask for IG probe into Pentagon's use of COVID-19 funds MORE (D-Calif.) says isn’t required under the rules.

But Republicans argue a formal vote would give them more leeway to call their own witnesses, and put swing-district Democrats on the record.