"To the extent Cohen might have been able to provide substantial assistance, those efforts were completely undermined by his inability to be truthful both with this office and in his public statements," the prosecutors said in a filing in Manhattan federal court.
Cohen last week asked a judge to cut his three-year sentence to a year and a day, saying he deserved credit for helping federal, state and Congressional investigators on matters related to Trump.
In their filing, however, prosecutors said Cohen "never made a meaningful effort to engage in serious cooperation but instead engaged in a protracted public relations campaign, in which he sought to cast himself as both victim and hero."
They said Cohen made false statements to prosecutors even after he was sentenced, which included saying that he had never sought a role in Trump's administration following the president's November 2016 election.
In fact, prosecutors said, both a television interview and private communications in the weeks after Trump's election showed that he had hoped to become White House chief of staff, and was disappointed when he did not get the job.
A lawyer for Cohen could not immediately be reached for comment.
Cohen, 52, pleaded guilty in 2018 to crimes that included violating campaign finance laws by directing hush-money payments shortly before the 2016 election to two women who said they had sexual relationships with Trump. The president has denied the relationships.
He also pleaded guilty to lying to Congress about a proposed Trump tower project in Moscow in a separate case brought by the office of Special Counsel Robert Mueller, which was investigating contacts between the Trump campaign and Russia.He began serving his prison sentence in May.