"When I heard his plea included information about keeping Donald Trump's kids up to speed, I have to say - we've heard this before - but I was thinking to myself, "lordy, I hope there are tapes" because we don't know what Michael Cohen has been taping but we may hear more about that in the future", he said.
"Michael's decision to cooperate and take full responsibility for his own conduct well reflects his personal resolve, notwithstanding past errors, to re-point his internal compass true north toward a productive, ethical and thoroughly law abiding life", his lawyers wrote.
They said Cohen is also cooperating with prosecutors from the U.S. attorney's office "concerning an ongoing investigation", the NY state attorney general's office's civil lawsuit against the Trump Foundation and state tax authorities.
Cohen pleaded guilty on Thursday to lying to Congress about the Russia investigation in a new deal with Mueller, who is probing Russian meddling during the 2016 presidential election.
In addition to his cooperation with Mueller, Cohen has also assisted in the NY state attorney general's investigation into the Trump Foundation, his lawyers revealed Friday, and has provided documents to the state attorney general in a separate, unidentified probe, too.
Cohen's false statements to Congress and his assistance to Trump with the hush-money payments arose out of his "fierce loyalty" to Trump, the lawyers wrote.
They say he'll continue to cooperate, though he wants to be sentenced as scheduled on December 12 so he can return to providing for his family.
Cohen admitted that he made the misstatements about the "Moscow Project" - the Trump Organization's efforts to "pursue a branded property in Moscow" in an August 2017 letter to the House and Senate intelligence committees, which were conducting inquiries into alleged collusion and Russian interference, according to court documents.
"That determination has not been made yet", Prosecutor Andrew Weissmann said at a federal court hearing in Washington. "To the contrary, he expects to cooperate further", the memo states.
"Nearly every professional and commercial relationship that he enjoyed, and a number of long standing friendships have vanished", it reads.
The lawyers portrayed Cohen as courageous for cooperating in Mueller's probe while the "investigation - and the rationale for its very existence - is regularly questioned publicly and stridently by the President of the United States".
"He and Client-1 also discussed possible travel to Russian Federation in the summer of 2016, and Michael took steps to clear dates for such travel", Cohen's lawyers said in the filing.
"Michael regrets that his vigor in promoting [Trump]'s interests in the heat of political battle led him to abandon good judgment and cross legal lines", the lawyers wrote. He then spoke by phone with one of Peskov's assistants.
Peskov told NBC that there were "two emails and one telephone call, returned telephone call, asking what they wanted and why they wanted to be in contact with [the Russian] presidential administration" but that "they did disappear".
The memo noted that Mueller's office is expected to provide the judge with an assessment of Cohen's cooperation, and that the Manhattan prosecutors are to join in presenting Cohen's assistance as a factor for the judge to consider.