Donald Trump’s former personal lawyer Michael Cohen, should spend a substantial term in prison for paying hush money to an adult actress on behalf of the president, prosecutors have said, despite him cooperating with the special counsel investigation into Russian interference in the election.

Cohen, 57, who once said he would “take a bullet” for the president, has been cooperating with two groups of investigators, one probing the lawyers payment of hush money to Stormy Daniels on the eve of the 2016 election, and Robert Mueller’s investigation into Moscow’s alleged actions and possible collusion with the Trump campaign.

While Mr Mueller said in a sentencing document that Cohen had gone to “significant lengths” to assist his probe, prosecutors in the southern district of New York said Cohen had not entered into a cooperation agreement with their office and that his sentence should reflect a “modest” reduction from the roughly four to five years they said federal guidelines would suggest.

Cohen did provide information to law enforcement, including information that assisted the special counsel’s office (SCO) in ongoing matters, as described in the SCO’s memorandum to the court, and the office agrees that this is a factor to be considered by the court,” wrote prosecutors in New York.

“But Cohen’s description of those efforts is overstated in some respects and incomplete in others. To be clear: Cohen does not have a cooperation agreement…and therefore is not properly described as a “cooperating witness,” as that term is commonly used in this district.”

It added: “While the office agrees that Cohen should receive credit for his assistance in the SCO investigation, that credit should not approximate the credit a traditional cooperating witness would receive, given, among other reasons, Cohen’s affirmative decision not to become one. For these reasons, the Office respectfully requests that this court impose a substantial term of imprisonment.”

This summer, Mr Cohen pleaded guilty to charges of tax evasion, bank fraud, and campaign finance violations in a case brought by the US Attorney’s Office for the Southern District of New York. Those campaign finance charges were about hush money payments Mr Cohen arranged in 2016 for women who alleged sexual encounters with Mr Trump, among them Ms Daniels.

Cohen pleaded guilty last week to a separate charge by brought by Mr Mueller’s office that he lied to Congress about discussions over the construction of a proposed Trump Organisation skyscraper in Moscow – referred to in court documents as the “Moscow Project”.

Donald Trump's former lawyer Michael Cohen has pleaded guilty to making false statements in relation to the Russia investigation and lying to Congress

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”.

Indeed, Mr Mueller said Cohen, who is scheduled to be sentenced next Wednesday by US District Judge William Pauley in Manhattan had provided considerable insight into the Trump campaign’s working.

“The defendant’s lies to Congress were deliberate and premeditated. His false statements did not spring spontaneously from a line of examination or heated colloquy during a congressional hearing. They started in a written submission that he chose to provide to both houses of Congress ahead of his appearances,” writes Mr Mueller.

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Mr Mueller said Mr Cohen had assisted in four specific areas – providing information about his own contacts with Russian interests during the campaign, providing information concerning certain “discrete Russia-related matters” core to the investigation, giving information concerning his contacts with persons connected to the White House during the 2017–2018 time period and describing the circumstances of preparing and circulating his response to the congressional enquiries.

“The defendant’s crime was serious, both in terms of the underlying conduct and its effect on multiple government investigations,” said Mr Mueller.

“The sentence imposed should reflect the fact that lying to federal investigators has real consequences, especially where the defendant lied to investigators about critical facts, in an investigation of national importance.”