The suit specifically alleges that both Trump and Giuliani violated what's often referred to as the Ku Klux Klan Act, which was passed in 1871 and is aimed at protecting against conspiracies created to obstruct constitutional duties.
Earlier on Tuesday, Bennie Thompson, chairman of the House Homeland Security Committee, filed a lawsuit accusing Trump of inciting the insurrection at the U.S. Capitol and of conspiring with his personal lawyer Rudy Giuliani and extremist groups including the Proud Boys and the Oath Keepers to try to prevent the Congress from certifying Joe Biden's presidential election victory.
It claims that Trump, Giuliani, the Proud Boys and the Oath Keepers conspired to incite a mob, march on the Capitol and through force, intimidation and threat prevent Congress' counting of the Electoral College votes.
The suit, backed by Mississippi Congressman Bennie Thompson and other members of Congress, was filed in Federal District Court in Washington, D.C. on Tuesday.
It was that claim, both McConnell and Democrats say, which incited the unprecedented attack on Congress on January 6.
"Trump is still liable for everything he did while he was in office, as an ordinary citizen, unless the statute of limitations has run [out]", McConnell said after his vote to acquit.
The Jan. 6 mob that descended on the Capitol was attempting to stop certification of Electoral College results declaring Joe Biden victor of November's presidential election.
It was Trump's longest statement since leaving office Credit AFP
The former president also faces potential legal repercussions for his January phone call to Georgia Secretary of State Brad Raffensperger, in which Trump pressured the official to "find" additional votes in an attempt to overturn the state's election results.
There was no immediate comment from Giuliani. MS congressman Rep Bennie Thompson and the National Association for the Advancement of Colored People (NAACP) are behind the legal action.
After witnessing Capitol police barricading the doors of the House chamber with furniture, Thompson and fellow lawmakers donned gas masks and were rushed into the Longworth House Office Building where they sheltered with more than 200 other representatives, staffers and family members.
Giuliani did not represent Trump in his impeachment trial because the attorney was a "witness" in the case and gave a speech at the pro-Trump rally that preceded the Capitol attack in which he told the crowd it was time for "trial by combat".
"President Trump has been acquitted in the Democrats' latest Impeachment Witch Hunt, and the facts are irrefutable", he said.