While speaking with Fox News hosts Harris Faulkner and Bill Hemmer about the passing of conservative radio personality Rush Limbaugh on Wednesday, Trump answered questions about the late radio personality's take on the 2020 United States presidential election, once again insisting that he had "won" on November 3.
Trump had attacked McConnell on Tuesday in retaliation to the GOP leader's public condemnation of the ex-president's incitement of the violent siege of the Capitol in January.
Mr McConnell's office on Tuesday declined to comment on Mr Trump's attacks, but the senator has left little mystery about his contempt for the former president.
"This is a big moment for our country", Trump wrote, "and we can not let it pass by using third rate "leaders" to dictate our future".
A report from The Washington Post cited sources familiar with Trump's thinking.
One person close to Mr Trump said his initial version of the statement was more incendiary than what was released publicly.
McConnell did not vote to convict Trump of inciting the insurrection in the impeachment trial that followed.
The 600-word statement, coming three days after the Senate acquitted Mr Trump in his second impeachment trial, was trained exclusively on Mr McConnell and sought to paint Mr Trump as the best leader of the Grand Old Party (GOP) going forward.
"My only regret is that McConnell "begged" for my strong support and endorsement before the great people of Kentucky in the 2020 election, and I gave it to him", Mr Trump said. "We don't have a snowball's chance in hell of taking back the majority without Donald Trump". However, he voted later that day to acquit the former U.S. president on the single impeachment charge of "incitement of insurrection". In remarks on the Senate floor shortly after Trump was cleared in a 57-43 vote, McConnell suggested that the former President could be subject to criminal prosecution.
In his statement on Tuesday night, Mr Trump argued that Mr McConnell bore responsibility for Republicans losing control of the Senate in November because he refused to sanction larger direct payments for Americans in a coronavirus relief package.
In the last weeks of Trump's presidency, the relationship between the then-Senate majority leader and Trump - the two most powerful men in the Republican Party - had essentially collapsed, multiple sources told CNN.
Trump's push comes as House Minority Leader Kevin McCarthy, a California Republican, is working to shore up his relationship with the ex-President, including meeting with Trump at his Palm Beach resort, Mar-a-Lago, in January.