Cohen, who has been cooperating with U.S. Special Counsel Robert Mueller's probe into possible collusion between Russian Federation and Trump's 2016 election campaign, pleaded guilty to the charges in August.
In addition to coming clean on the Moscow project, Cohen provided information to Mueller about several attempts by Russians to contact the Trump's campaign, according to Friday's filing.
"Totally clears the president".
The situation is complicated by the fact that Mr Trump, who has railed against the "witch hunt, recently sacked his attorney general, Jeff Sessions, and replaced him with an arch critic of the Mueller probe, Matthew Whitaker".
Robert Mueller, the special counsel heading up the probe into Russian meddling in the 2016 vote, followed up with a separate filing saying Cohen had made "substantial and significant efforts to remediate his misconduct, accept responsibility for his actions, and assist" the special investigation, a thorn in Trump's side.
So Cohen actually saying he was doing it at Trump's request isn't new.
That was a reference to a proposed Moscow real estate deal that prosecutors say could have netted Trump's business hundreds of millions of dollars.
Mueller's memo is not giving a specific sentencing recommendation, but because Cohen is being cooperative and has accepted responsibility for his lies, his office is requesting that any prison time for which he might be sentenced for misleading Congress be run concurrently with the sentences he gets for his fraud and campaign violation plea bargain with the NY office.
The memo said while prosecutors agree that Cohen should receive credit for his assistance with the special counsel's office, since he chose not to be a formal cooperating witness, he would only get a modest reduction in sentence.
In August, 52-year-old Cohen pleaded guilty to violating campaign finance law in connection with the payments.
"In his interviews with the Special Counsel's Office and the FBI, Manafort told multiple discernible lies - these were not instances of mere memory lapses", Mueller's office said in the filing.
A heavily redacted court filing said that Manafort's "lies" included untruths about his dealings with Konstantin Kilimnik, a business associate who USA officials suspect is a Russian intelligence operative, and about his contacts with Trump administration officials after striking a plea agreement.
In Manafort's case, prosecutors are expected to lay out what torpedoed the cooperation agreement he made when he pleaded guilty in September to two felony charges of conspiracy.
Manafort resigned from his job on the Trump campaign as questions swirled about his lobbying work for a pro-Russia political party in Ukraine.
The Cohen memo prosecutors released Friday lists three people at an August 2014 meeting: Cohen, "Individual-1" and "Chairman-1". "But Cohen's description of those efforts is overstated in some respects and incomplete in others".
"After cheating the IRS for years, lying to banks and to Congress, and seeking to criminally influence the presidential election, Cohen's decision to plead guilty - rather than seek a pardon for his manifold crimes - does not make him a hero", they wrote.
He said Trump had directed him before the 2016 election to arrange payments to buy the silence of porn actress Stormy Daniels and former Playboy model Karen McDougal, both of whom alleged they had affairs with Trump. Though Cohen had previously implicated Trump in the payments, the prosecutors now are linking Trump to the scheme and backing up Cohen's allegations.
Attorneys from the Southern District of NY state explicitly in the court filing that Cohen "acted in coordination with and at the direction of Individual-1" in handling payments to two women who claimed to have an affair with Trump long before the election.