NEW YORK – Federal prosecutors on Friday sharply criticized President Donald Trump's ex-personal attorney Michael Cohen, saying he should serve "a substantial prison term" for trying to buy the silence of two women who said they had sexual affairs with Trump, for evading federal income taxes and for lying to banks.

In a sentencing memo, the prosecutors from the Southern District of New York outlined four different federal crimes committed by Cohen over several years, writing that he "repeatedly used his power and influence for deceptive ends."

Special Counsel Robert Mueller took a softer approach in a separate sentencing memo. He credited Cohen for correcting his lies to Congress about plans to build a Trump Tower in Moscow – and for going to "significant lengths" to assist Mueller's investigation of Russia-related matters that touched on Trump's 2016 presidential campaign.

The memos submitted to U.S. District Judge William Pauley provided details of the crimes to which Cohen has pleaded guilty, his cooperation with the special counsel, and what prosecutors think it was worth.

They also recounted Cohen's interaction with Trump as the attorney committed crimes. The New York prosecutors wrote that Cohen violated campaign finance laws "in coordination with and at the direction of Individual-1" – Trump.

And Mueller's team wrote that "the fact that Cohen continued to work on the [Moscow] project and discuss it with Individual 1 well into the campaign was material" to investigations by Congress and the special counsel "particularly because it occurred at a time of sustained efforts by the Russian government to interfere with the U.S. presidential election."

Pauley is scheduled to sentence Cohen on Wednesday. He asked last week to be spared prison time for his cooperation. But the prosecutors in New York said he should serve roughly 42 months.

The prosecutors said Cohen deserved some credit for providing information to Mueller and other investigators. But they also criticized him for maintaining what they called a "rose-colored view" of his conduct.

"The crimes committed by Cohen were more serious than his submission allows and were marked by a pattern of deception that permeated his professional life," they wrote.

They stressed that Cohen does not have a formal cooperation agreement with the Manhattan U.S. Attorney's Office, and argued he should not get the leniency that "a traditional cooperating witness would receive."

"After cheating the IRS for years, lying to the 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 concluded.

Mueller's legal team wrote that Cohen provided "a detailed account of his involvement and the involvement of others in the Moscow Project," as well as information "about attempts by other Russian nationals to reach the campaign" run by Trump.

The team said Cohen disclosed new information showing that he was in touch with a Russian national who claimed to be a "trusted person" in the Russian Federation around November 2015, an earlier contact with a Trump campaign member than previously known.

According to the Mueller team memo, the individual offered to provide the Trump campaign with "synergy on a government level," and proposed a meeting between "Individual 1 and the President of Russia," Vladimir Putin.

Cohen did not follow up on the invitation because he was working on the Moscow project with a different person whom he believed had connections to the Russian government, the memo said.

Additionally, the team wrote, Cohen provided "relevant and useful information about his contacts with people connected to the White House" during Trump's first two years in office, and about "certain discrete Russia-related matters" that are core to the special counsel's investigation.

As a result, Mueller's office said it would be "appropriate" if any sentence that Cohen got for lying to Congress ran concurrently with the sentence imposed for the crimes investigated by New York federal prosecutors.

Pauley will have to reconcile the disparate views represented in the sentencing memos.

The sentencing memos represent the latest development in Mueller's investigation of an alleged conspiracy between Trump's presidential campaign and Russia, and for the pugnacious attorney long known as an ardent Trump loyalist and fixer of difficult problems.

The relationship between Cohen and Trump ruptured this year as Cohen pleaded guilty to campaign finance violations, fraud and lying to Congress while Trump continued to brand Mueller's investigation as a witch hunt.

Cohen pleaded guilty in August to violating campaign finance laws by paying hush money at Trump's direction to adult film star Stormy Daniels and former Playboy model Karen McDougal.

Trump has denied the women's accounts.

More:Here's a look at Michael Cohen's allegations about President Donald Trump

More:Trump goes after former lawyer, Michael Cohen, but sides with Roger Stone

The New York-based prosecutors alleged in August that the payments were made "in order to influence the 2016 presidential election," and were "coordinated with one or more members" of Trump's winning campaign, "including through meetings and phone calls about the fact, nature, and timing."

Cohen also pleaded guilty in August to charges of tax evasion and making false statements to federally insured banks. Prosecutors say he lied to banks to obtain loans and lied to the government to avoid paying taxes.

The prosecutors said Cohen failed to report more than $4 million in income to the IRS from tax years 2012 through 2016. They said he hid income from his accountant and the IRS, allowing him to duck more than $1.4 million in tax payments.

Separately, they said, Cohen hid millions of dollars in debts and made false statements about his net worth and monthly expenses when he applied to banks for loans.

Cohen pleaded guilty last week to charges that he lied to congressional committees investigating Trump's dealings with Russia.

He told the Senate and House panels last year that planning for a Trump Tower in Moscow, discussions about a possible Trump trip to Russia in connection with the project, and related talks with Russia officials all ended in January 2016.

That meant the subject was dropped before the Iowa caucuses in February, the first political battlefield in the 2016 presidential race.

But Cohen admitted last week that he continued to discuss efforts to win Russian governmental approval for the project within The Trump Organization as late as June 2016. By then, Trump was the presumptive Republican presidential nominee.

Cohen also said he agreed to travel to Russia for the construction plan, and asked Trump about the possibility of him traveling there, too.

Mueller's team wrote that the lies to Congress were "deliberate and premeditated."

After deciding, in an abrupt turnaround, to cooperate with investigators, Cohen provided the special counsel's team with "information about his own conduct and that of others" regarding Russia-related issues, Mueller's team wrote.

"The information he has provided has been credible and consistent with other evidence obtained" in the Russia investigation, the team wrote.

In the separate sentencing memo filed by Cohen's defense team last week, attorneys Guy Petrillo and Amy Lester provided additional detail about what they characterized as the initial "false summary" about the Moscow project.

The attorneys appeared to implicate Trump, referred to as the "client" or "Client-1," in some of Cohen's crimes.

"Michael had a lengthy substantive conversation with the personal assistant to a Kremlin official following his outreach in January 2016, engaged in additional communications concerning the project as late as June 2016, and kept Client-1 apprised of these communications," Petrillo and Lester wrote.

Cohen and Client-1 "also discussed possible travel to Russia in the summer of 2016, and Michael took steps' to clear dates for such travel," they wrote.

Regarding the hush money, Cohen's attorneys wrote that he did not personally make payments to buy the silence of "Woman-1," apparently McDougal.

But they wrote that he "participated in payment planning discussions with Client-1 and the Chairman and CEO of Corporation-1."

McDougal said The National Enquirer paid her for her story but did not publish it. The supermarket tabloid is owned by American Media, which is led by Trump friend David Pecker.

The attorneys described a similar effort to prevent Daniels, whose real name is Stephanie Clifford, from publicizing her claims about a sexual fling with Trump.

Cohen paid Daniels "in coordination with and at the direction of Client-1, and others within" The Trump Organization, they wrote.

Cohen's attorneys asked for leniency based on his voluntary cooperation with the investigations by Mueller and federal prosecutors, and with Trump-related investigations by the New York Attorney General's Office and the New York State Department of Taxation and Finance.

They stressed that Cohen had owned up to personal wrongdoing instead of joining Trump's continuous criticism and questioning of Mueller.

"He could have fought the government and continued to hold to the party line, positioning himself for a pardon or clemency," Petrillo and Lester wrote. "But, instead — for himself, his family, and his country — he took personal responsibility for his own wrongdoing and contributed, and is prepared to continue to contribute, to an investigation that he views as thoroughly legitimate and vital."

Follow USA TODAY reporter Kevin McCoy on Twitter: @kmccoynyc