Michael Cohen's legal advisor on Thursday called for President Donald Trump to be censured by Congress for "witness tampering" one day after Trump's ex-lawyer postponed his congressional testimony due to "threats" against his family by the president.

Cohen advisor Lanny Davis also asked for a criminal probe of Trump's current personal lawyer, Rudy Giuliani, for similar alleged threatening remarks. He said comments by Trump and Giuliani have left Cohen in fear for the safety of his family.

"Today I am calling for an immediate House resolution against Trump for congressional witness tampering and obstruction due horrible multiple threats to Michael's family, and an immediate criminal investigation and possible indictment of Giuliani for the same conduct, since he does not have likely presidential immunity," Davis said in a statement to CNBC.

Davis first made his requests public earlier Thursday on ABC's "Good Morning America."

"Let's call this what it is, a petty partisan move from a partisan attorney to his fellow partisans in the House of Representatives — and the American people see right through it," Hogan Gidley, White House deputy press secretary, told CNBC.

Also Thursday, Trump in a tweet blasted his former attorney and longtime fixer Cohen as a "bad lawyer."

The president also referenced Davis in the tweet, calling him "the lawyer for Crooked Hillary Clinton." Davis is a long-time friend and advisor to former President Bill Clinton and former Secretary of State Hillary Clinton, whom Trump defeated in the 2016 presidential election.

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Cohen, 52, had been scheduled to testify before the House Oversight Committee on Feb. 7, a month before he begins serving a three-year prison terms of multiple crimes.

Those felonies included ones related to hush-money payments that Cohen facilitated to two women, porn star Stormy Daniels and Playboy model Karen McDougal, shortly before the 2016 presidential election to keep them quiet about alleged affairs with Trump. The president has denied having sex with either woman.

Cohen also admitted to the crime of lying to Congress by making misleading statements about the duration of an aborted effort to build a Trump Tower in Moscow, and about the extent of Trump's involvement in the project.

Cohen, who has been cooperating with special counsel Robert Mueller's probe of Trump and possible coordination by members of Trump's campaign with Russian interference in the 2016 election, was expected to talk at length about the president during his planned congressional appearance.

Davis announced Wednesday that Cohen was indefinitely postponing that appearance, citing "ongoing threats against his family from President Trump and Mr. Giuliani."

On Thursday morning, Cohen was subpoenaed by the Senate Intelligence Committee to testify at a hearing reportedly set for Feb. 12.

Trump repeatedly has made public mention of Cohen's father-in-law, Fima Shusterman, who was placed on probation in the mid-1990s after pleading guilty in a case in which he was charged with conspiring to defraud the IRS.

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Giuliani, in an appearance Sunday on CNN, claimed Cohen had lied lying about Trump, suggested that Shusterman had organized crime connections, and alleged that Shusterman was involved in criminal activity with Cohen.

Despite those claims by Giuliani, a former New York mayor and federal prosecutor, Shusterman and Cohen have not been charged with any crimes related to each other, and Shusterman has not be charged with any organized crime activity.

Trump on Wednesday was dismissive of Davis' claims that he had threatened Cohen.

"I would say he's been threatened by the truth," Trump said. "He has other clients also, I assume, and he doesn't want to tell the truth for me or other of his clients."

The president has denied any wrongdoing by himself or by his campaign. He has repeatedly claimed there was "no collusion" with Russia to help get him elected.

Trump and Giuliani had made complimentary comments about Cohen on the heels of an April 2018 raid by the FBI on Cohen's office and residences in New York. But their tone changed after Cohen appeared to break with the president, a move that was underscored by his retention of the Clinton confidante Davis, a harsh critic of Trump.

House Oversight Committee Chairman Elijah Cummings, D-Md., and Intelligence Committee Chairman Adam Schiff, D-Calif., said Wednesday that Cohen's concern for the safety of his family was "legitimate," but added that they expected him to testify before their committees at some point.

Cummings and Schiff also blasted Trump's comments.

"As we stated previously with our colleague, Chairman Jerry Nadler of the Judiciary Committee, efforts to intimidate witnesses, scare their family members, or prevent them from testifying before Congress are textbook mob tactics that we condemn in the strongest terms," Cummings and Schiff said in a joint statement.

"Our nation's laws prohibit efforts to discourage, intimidate, or otherwise pressure a witness not to provide testimony to Congress. The President should make no statement or take any action to obstruct Congress' independent oversight and investigative efforts, including by seeking to discourage any witness from testifying in response to a duly authorized request from Congress."