Trump launched the latest salvo on Fox Business Network, when his interviewer asked about the upcoming mid-term election battle for control of the Senate and House of Representatives.
"We need good leadership. Mitch McConnell has not done a great job. I think they should change Mitch McConnell," the former president said.
Asked about Trump's comments, McConnell told Fox News Channel: "We're looking to the future, not the past."
Related: Trump attacks Pence, McConnell in speech to party donors
The Kentucky Republican has led his caucus in the Senate without opposition since 2007.
Bad blood between Trump and McConnell could complicate matters for Republicans as they try to reclaim the Senate majority, with both voters and lawmakers divided between Trump loyalists and the traditional party.
Democrats took control of the Senate in January by winning two seats in Georgia, after Trump stirred divisions by pushing the false claim that the 2020 election had been stolen from him and attacking Republican state officials for not overturning the results.
The 100-seat Senate is currently divided 50-50 between Republicans and Democrats, with Democratic Vice President Kamala Harris wielding the tie-breaking vote. But Democrats are well aware that the party that controls the White House historically loses seats in Congress in the first election of a presidency.
McConnell drew Trump's ire by acknowledging that President Joe Biden had won and by blaming Trump for the deadly Jan. 6 attack on the U.S. Capitol after the Senate acquitted the former president on a charge of inciting insurrection.
Less than a month ago, Trump called McConnell "a son of a bitch" at a dinner for Republican National Committee donors at his Mar-a-Lago Club, according to an attendee.
(Reporting by David Morgan; Editing by Sonya Hepinstall and Richard Pullin)
