George Conway, the husband of White House counselor Kellyanne Conway, disputed President Trump’s claim of being “totally” cleared of wrongdoing Friday in the government’s case against his former personal lawyer and fixer Michael Cohen.

A conservative attorney and vocal critic of Mr. Trump, Mr. Conway mocked the president on Twitter over his reaction to a sentencing document filed by federal prosecutors detailing Mr. Cohen’s admitted criminal conduct.

“Totally clears the President,” Mr. Trump tweeted Friday evening. “Thank you!”

“Except for that little part where the U.S. Attorney’s Office says that you directed and coordinated with Cohen to commit two felonies,” responded Mr. Conway. “Other than that, totally scot-free.”

Filed by prosecutors in the Southern District of New York, Friday’s sentencing memo said that Mr. Cohen admitted that he paid hush money during the 2016 presidential race to two women who alleged having affairs with Mr. Trump, and that the payments were made in “coordination with and the direction of” Mr. Trump, referenced in the document as “individual 1.”

“This is the first time that the government has alleged in its own voice that President Trump is personally involved in what it considers to be federal offenses,” Mr. Conway retweeted another Twitter user remarking.

Mr. Cohen, 52, pleaded guilty to eight counts of bank fraud, tax fraud and campaign finance law violations in Aug. 2018. Prosecutors requested a “substantial term of imprisonment” when he is sentenced later this month.

“The government’s filings in Mr. Cohen’s case tell us nothing of value that wasn’t already known,” White House press secretary Sarah Huckabee Sanders said in a statement. “Mr. Cohen has repeatedly lied and as the prosecution has pointed out to the court, Mr. Cohen is no hero.”

Mr. Conway, 55, married the president’s counselor in 2001. He has been frequently critical of Mr. Trump on Twitter, drawing rebuke last week from one of the president’s sons.

“Of all the ugliness in politics, the utter disrespect George Conway shows toward his wife, her career, place of work, and everything she has fought SO hard to achieve, might top them all,” Eric Trump tweeted last week.