Mr Rosen assumed his position in the final weeks of Mr Trump's presidency after William Barr resigned effective 23 December, 2020, rather than use the department to pursue Mr Trump's false claims, which were rejected by multiple courts, state election officials and his own administration.
"Today's report shows the American people just how close we came to a constitutional crisis," Senate Judiciary Committee Chairman Dick Durbin said in a statement.
Mr Rosen told the committee that Mr Trump opened one meeting with him by saying, "One thing we know is you, Rosen, aren't going to do anything to overturn the election."
Mr Trump also asked Mr Clark if he would be willing to take over as acting attorney general, the report said, adding that Mr Clark relayed this message to Mr Rosen.
"Rosen recalled Clark indicating that he hadn’t yet decided whether he would accept Trump’s offer, wanted to conduct some 'due diligence' on certain election fraud claims, and might turn down the offer if he determined that Rosen and (Rosen's deputy, Richard Donoghue) were correct that there was no corruption," the report said.
The report also found that Mr Clark sought to attend a meeting with the Office of the Director of National Intelligence to ask about a baseless conspiracy theory that a Dominion voting machine "accessed the Internet through a smart thermostat."
Mr Clark pushed for a letter to Georgia, urging a special legislative session to contest the election results, the report said. The request was refused.
Mr Clark's efforts ultimately failed, after all of the department's remaining senior leadership threatened to resign in protest if Mr Clark were installed.
Mr Durbin said the committee has asked Mr Clark to testify.
Thursday's report also contains new details about how former White House Chief of Staff Mark Meadows tried to convince Mr Rosen to launch "at least four categories of false election claims" in places such as Fulton County, Georgia and New Mexico.
Republicans on the committee issued their own report, which drew different conclusions.
"The available evidence shows that President Trump did what we’d expect a president to do on an issue of this importance: He listened to his senior advisers and followed their advice and recommendations," Ranking Member Charles Grassley said.