WASHINGTON — Facing mounting criticism for blocking proposals to bolster election security, Senator Mitch McConnell on Thursday threw his weight behind a new infusion of $250 million to help states guard against outside interference in the 2020 voting.

Mr. McConnell, Republican of Kentucky and the majority leader, has been under regular attack from both Democrats and a conservative group for refusing to allow the Senate to vote on various election security proposals, some of them bipartisan, despite dire warnings from the intelligence community that Russia is already trying to replicate the elaborate meddling campaign it carried out during the 2016 presidential contest.

The additional funding, Mr. McConnell said in announcing his support, “will bring our total allocation for election security — listen to this — to more than $600 million since fiscal 2018.” The money was quickly approved by the Appropriations Committee later Thursday.

Though Mr. McConnell has embraced other seemingly derogatory nicknames over the years, he was incensed at being called “Moscow Mitch” by those who claimed his opposition showed he was willing to accept foreign election interference because it had benefited his own party by helping to elect President Trump, despite the senator’s long record of taking a hard line against Russia.