Updated at 5:55 p.m. ET

The government is seeking a "substantial term of imprisonment" for Donald Trump's former lawyer Michael Cohen, it said in court documents submitted on Friday — but would like a judge to give consideration to cooperation he has rendered in the Russia and other investigations.

Prosecutors working for the U.S. Attorney's Office for the Southern District of New York based in Manhattan asked a judge to impose a sentence that reflects a "modest downward variance" from the potential maximum of 63 months in prison that Cohen faces.

Although Cohen has been cooperating with investigators in New York City and with the office of Justice Department special counsel Robert Mueller, he does not have a full cooperation agreement with the government.

Mueller's office, in a separate filing, did not take a position on what sentence Cohen should receive when he appears before a judge next week in New York City.

Mueller's filing did, however, acknowledge Cohen's help in the Russia investigation and also said that he has provided new information about contacts between Trump's presidential campaign and Russians, including outreach as early as November 2015 from people seeking to arrange meetings between Trump and Russian President Vladimir Putin.

The meeting did not take place.

Cohen has pleaded guilty to lying to Congress about negotiations between Trump's business and powerful Russians about a possible deal for a Trump Tower in Moscow, a building that ultimately was never built.

Cohen, however, initially told Congress that the talks had stopped by January of 2016. Actually, he said in his guilty plea, they continued well into the campaign, including past the point at which Trump became the Republican front-runner.

The crafting of that narrative was a "deliberate effort to use his lies as a way to set the tone and shape the course of the hearings in an effort to stymie the inquiries," the special counsel's office said.

Cohen wanted to obscure from Congress and the public that if the project had been completed, Trump's company "could have received hundreds of millions of dollars from Russian sources in licensing fees and other revenues," prosecutors wrote.

They continued: "The fact that Cohen continued to work on the project and discuss it with [Trump] well into the campaign was material to the ongoing congressional and [special counsel] investigations, particularly because it occurred at a time of sustained efforts by the Russian government to interfere with the U.S. presidential election."

Mueller's office has been tasked with investigating whether anyone in Trump's campaign conspired with the Russians who were waging those "active measures" against the United States and the West.

Trump says his campaign had nothing to do with the Russian election interference and he denounces Mueller's investigation as a "hoax" and a "witch hunt."

Trump repeated his criticism again on Friday and said on Twitter that his attorneys have already begun work on a rebuttal to Mueller in case the special counsel's report is damaging to Trump and becomes public.

Trump also has focused his criticism specifically on Cohen, calling him a liar who is making up stories to convince the government to ease his sentence in another federal case filed in New York City to which he's also pleaded guilty.

The president has acknowledged "lightly" looking into a Trump Tower project in Moscow but said that broke no law and that he was perfectly within his rights to continue to operate his real estate business at the same time his presidential campaign was picking up steam.

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