Bennie Thompson in his personal capacity, is the first civil action filed against the former President related to the attack at the US Capitol and comes days after the Senate acquitted Trump in his impeachment trial.
"The Republican Party can never again be respected or strong with political "leaders" like Sen".
"Mitch is a dour, sullen, and unsmiling political hack, and if Republican Senators are going to stay with him, they will not win again", he added.
Some, like the seven Republican senators who voted to convict Trump during the second impeachment trial, have sought to distance the party from the former president.
The deeply personal attack follows McConnell's speech over over the weekend saying that Trump was responsible for the deadly insurrection at the Capitol on January 6.
The two are trying to push the party in opposite directions, McConnell back toward the roots of a budget-focused, pro-trade party, while Trump, who is still backed by a large portion of the Republican voter base, advocates a more populist approach. "Mitch McConnell at its helm", Mr Trump said in a statement.
The senator was quick to note that he was not lumping "the hundreds of violent mob rioters" that attacked the federal seat of government with the 74 million Americans who cast ballots for the former president.
But he used the blast against Mr McConnell to assert his continuing claim to leadership of the Republican party.
"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".
After 50 Democratic senators and seven Republicans voted that Trump was guilty - a majority in the 100-seat Senate, but not the two-thirds needed for a conviction - McConnell let loose, excoriating Trump for the attack that saw five people die and the halls of the U.S. legislature ransacked by his supporters.
The suit traces the drawn-out effort by Mr Trump and Mr Giuliani to cast doubt on the election results even though courts across the country, and state election officials, repeatedly rejected their baseless allegations of election fraud.
"His behaviour during and after the chaos was also unconscionable".
The House impeached Trump a week before he left office.
The districts' actions set up a collision course with the state Republican Party organization, where chairman Glenn Clary has supported a "big tent" approach to party membership. We could sit here and talk about our problems with Donald Trump, but people who support him in little ecosystem bubbles, they don't hear us screaming that we're so fed up with what he did tonight and all of these things.
CNN reported last month that Trump is focusing his political energy on Rep. Liz Cheney of Wyoming, the third-ranking House Republican, who voted for his impeachment last month.