President Donald Trump's former lawyer, Michael Cohen, was in touch as far back as 2015 with a Russian who offered "political synergy" with his 2016 election campaign, the United States federal special counsel said on Friday in a court filing.

Filings by prosecutors also alleged that the president directed Cohen to make illegal payments to buy the silence of two women, whose claims of extramarital affairs threatened his presidential campaign.

Prosecutors from both New York and the Trump-Russia special counsel's office laid out for the first time details of the cooperation of Cohen, a vital witness who once said he'd "take a bullet" for the president but who in recent months has become a prime antagonist and pledged to come clean with the government.

In hours of meetings with prosecutors, Cohen detailed his intimate involvement in an array of episodes, including some that directly touch the president, that are at the centre of investigations into campaign finance violations and potential collusion between the Trump campaign and the Kremlin.

In one of the filings, Special Counsel Robert Mueller details how Cohen spoke to a Russian who "claimed to be a 'trusted person' in the Russian Federation who could offer the campaign 'political synergy' and 'synergy on a government level'".

The filing says the meeting never happened.

Mueller is investigating possible collusion between Russia and Trump's 2016 election campaign. 

'Substantial prison sentence'

Federal prosecutors said on Friday that Cohen deserves a substantial prison sentence for paying an adult film star hush money on Trump's behalf and evading taxes, despite his cooperation with investigators. He is to be sentenced next week and he may face several years in prison. Cohen pleaded guilty to those charges in August.

Prosecutors also detailed that Cohen arranged secret payments to two women at the height of the 2016 campaign "in coordination with and at the direction of" Trump.

The filing stopped short of accusing the president of committing a crime. Whether a president can be prosecuted while in office remains a matter of legal dispute.

But there's no ambiguity in Friday's filing that prosecutors believe Cohen's act was criminal and Trump was directly involved, a remarkable disclosure with potential political and legal ramifications for a president dogged by investigations.

The payments are likely to become a target for House Democrats gearing up to investigate the president next year. It's unclear whether Trump faces legal jeopardy over his role.

Federal law requires that any payments made "for the purposes of influencing" an election must be reported in campaign finance disclosures. The court filing on Friday makes clear that the payments were made to benefit Trump politically.

Last week, Cohen pleaded guilty to a separate charge by Mueller's office that he lied to Congress about discussions over the construction of a proposed Trump Organization skyscraper in Moscow.

In a separate filing on Friday, Mueller's office said Cohen should serve any sentence imposed for that crime concurrently with the sentence imposed for the New York charges, saying he had gone to "significant lengths to assist the Special Counsel’s investigation", although he initially lied. 

The New York prosecutors said in their filing that Cohen should receive some credit for his cooperation with Mueller, but noted that he had not entered into a cooperation agreement with their office. They said his sentence should reflect a "modest" reduction from the roughly four to five years they said federal guidelines would suggest.

Trump, who has called Mueller's investigation a "witch-hunt" and repeatedly denied wrongdoing, said earlier this week that Cohen had lied about Trump's business dealings in Russia to get reduced jail time.

White House Press Secretary Sarah Sanders said the government filings about Cohen "tell us nothing of value that wasn't already known". 

Mueller's office has charged or secured convictions against more than two dozen Russian nationals and entities, as well as a number of Trump's associates. The Manhattan prosecutors' charges against Cohen stemmed from a referral from Mueller's team.

Russia has denied meddling in the 2016 US election.

Manafort memo

Also on Friday, Mueller disclosed details of alleged lies told by Trump's former campaign manager, Paul Manafort, during interviews with prosecutors. 

Among other matters, they said Manafort lied about his interactions with a political consultant who had ties to Russian intelligence, and about interactions with Trump administration officials even after Manafort was indicted in late 2017.

"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 said in the filing, which was requested by a federal judge in Washington after Mueller accused Manafort of breaching his plea deal last month.

The new developments came just hours after Trump announced he had chosen former US Attorney General William Barr to once again lead the Justice Department, a role that would put him in charge of the Mueller's probe into Russian election interference.

If confirmed by the Senate, Barr would succeed Jeff Sessions, who was forced out by Trump last month. Sessions's chief of staff, Matthew Whitaker, is currently serving as acting attorney general.

The White House said the Manafort filing "says absolutely nothing about the president".