Russian Federation had denied interfering in the 2016 election.
Cohen this week completed meetings with congressional investigators looking into Trump's activities.
The discussion of a pardon was broached by Cohen's lawyer at the time, Stephen Ryan, who spoke with the president's attorneys in the months after the raid. "He's hiding behind having his lawyers do it", Giuliani said.
Michael Cohen testified last Wednesday before the House Oversight Committee in an open hearing.
Cohen's lawsuit also renews an allegation that's dogged Trump for much of his career: He has a penchant for cheating people out of money he had promised them.
Answers were divided along party lines: More than 20 percent of Republicans believe Trump committed crimes before he was president, compared to 89 percent of Democrats who say the same. But, he said, that would happen only after Mueller's work wraps up.
"Another perjury and more prison", Giuliani said on Twitter Thursday. Nobody is taking that away from him.
But despite written requests for reimbursement, the company has not paid him since May 2018, about the time Mr Cohen agreed to cooperate with the Special Counsel's investigation.
"Before his public testimony he spent time digging through boxes in a storage unit to find documents that backed up some of his claims", Fox continued, citing her own reporting.
'After July 2, 2018, Mr. Cohen authorized me as a new lawyer to say publicly Mr. Cohen would never accept a pardon from President Trump even if offered. "Lanny Davis coordinated and choreographed this whole thing", Jordan said.
Davis did not immediately respond Thursday to text messages and emails seeking additional information.
The lawsuit filed Thursday in NY state court claims the Trump Organization stopped paying Cohen's mounting legal fees after he began co-operating with federal prosecutors.
Earlier Friday, speaking to reporters on the White House lawn, he said that Cohen had told a "stone cold lie" when he testified that he did not seek presidential intervention.
"The Trump Organization doesn't owe Michael Cohen one penny of legal fees", he said.
This follows last week's hearing when Cohen alleged that Trump played a role in hush money payments to women that may have violated campaign finance laws.
Cohen was one of Trump's lawyers and closest advisers for a decade until their public split last summer. Trump has denied having an affair.