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.) avoided weighing in on whether Labor Secretary Alexander Acosta Alex Alexander AcostaFederal litigator files complaint alleging Labor secretary abused his authority Appeals court to review legality of Epstein plea deal Appeals court finds prosecutors' secret plea agreement with Epstein didn't break law MORE should resign over a 2008 plea deal involving financier Jeffrey Epstein, saying his fate is up to 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.

McConnell, asked if Acosta should step down, called the allegations against Epstein "horrendous," but avoided either defending or criticizing Acosta, who agreed to a plea deal in 2008 that allowed Epstein to avoid a life sentence.

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"There's no question that the accusations against Epstein are horrendous and I think it's good news that they're being pursued further. As to Secretary Acosta's continued service, he serves at the pleasure of the president and I'm inclined to defer the president to make that decision," McConnell said.

McConnell's comments come as Acosta is under growing fire, including from 2020 Democrats calling on him to resign, after federal prosecutors unsealed new sex trafficking charges against Epstein on Monday, alleging he abused dozens of girls. He has denied all charges.

The charges are being contrasted with a 2008 deal Acosta made when he was a U.S. attorney that allowed Epstein to serve 13 months in “custody with work release."

Republicans have largely stood by Acosta, who was confirmed by the Senate for the Labor Department spot in 2017, arguing that they reviewed the plea deal during his confirmation hearing.

Sen. John Thune John Randolph ThuneSenate passes resolution reaffirming commitment to peaceful transition of power Susan Collins faces political land mine with Supreme Court fight Abortion stirs GOP tensions in Supreme Court fight MORE (S.D.), the No. 2 Senate Republican, told reporters on Tuesday that Republicans haven't been raising too many concerns about Acosta privately.

"It really hasn't come up much. … If there's new information now and a stronger case and he can be more fully prosecuted, I think everybody is amenable to that. But I just don't think at this point there's been a lot of conversation among our members about it beyond what they're reading in the reports," Thune told reporters.