Trump slammed both Cohen and Mueller in a series of tweets shortly after Cohen pleaded guilty in federal court last Thursday.
Attorneys representing Jerome Corsi filed an ethics complaint Monday accusing prosecutors in Special Counsel Robert Mueller's office of pressuring their client to provide "false testimony" against Republican operative Roger Stone and President Trump.
While Washington is focused on memorializing former President George H.W. Bush, Mr. Trump on Monday morning, at least on Twitter, has been focused on whether his associates defend him or not.
Last week Trump's former personal lawyer Michael Cohen pleaded guilty to misleading Congress about Trump's plans to build a tower in Moscow and revealed he had entered into a formal co-operation agreement with Mueller.
Mr. Trump - who initially defended Cohen when federal investigators raided his apartment and office in April - has since appeared to turn on Cohen.
"He lied for this outcome and should, in my opinion, serve a full and complete sentence", Trump added.
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President Trump is responding to former campaign adviser Roger Stone's vow not to testify against him.
Trump meanwhile lashed out at Mueller, whom he again accused of forcing witnesses to make up lies damaging to him.
On Thursday, Cohen added an additional guilty plea, admitting that he lied to Congress about an ultimately unsuccessful effort to build a Trump building in Russian Federation.
Before last week, Trump had repeatedly said he had no business dealings in Russian Federation, tweeting in July 2016, "For the record, I have ZERO investments in Russian Federation", and telling reporters in January 2017 that he had no deals there because he had "stayed away".
There was a strong case against the president for witness tampering because of his prior acts and statements, like dangling the possibility of a pardon for his Manafort, legal experts said.
"The American people deserve to know how much of the Trump-Russia probe was the result of agent provocateurs and political muckrakers and FISA cheaters, and how much was legitimate law enforcement work", Solomon said. "The truth is very bad for their mission!" he also tweeted.