Michael Cohen, the president’s former lawyer who was recently sentenced to three years in prison, is postponing his highly-anticipated testimony before Congress next month because of “ongoing threats” from President Trump and his legal team, Cohen’s lawyer claimed Wednesday.

“This is a time where Mr. Cohen had to put his family and their safety first," Cohen lawyer Lanny Davis said in a statement.

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Davis said Cohen “looks forward to testifying at the appropriate time.” He claimed both the president and his lawyer, Rudy Giuliani, had threatened Cohen. Davis did not detail the alleged threats.

“Due to ongoing threats against his family from President Trump and Mr. Giuliani, as recently as this weekend, as well as Mr. Cohen's continued cooperation with ongoing investigations, by advice of counsel, Mr. Cohen’s appearance will be postponed to a later date,” Davis said.

Speaking to reporters at the White House, Trump shot back at Cohen: "He's only been threatened by the truth."

Rep. Elijah Cummings, the Democratic chairman of the Oversight Committee, and Rep. Adam Schiff, the chairman of the House Intelligence Committee, issued a joint statement saying, “We certainly understand the completely legitimate concerns for the safety and security of Mr. Cohen and his family members in light of the attacks last week by President Trump and again this past weekend by his attorney, Rudy Giuliani.” They added that they still expect Cohen to appear before their committees at a later date.

There has been great interest in Cohen’s testimony. The announcement follows Special Counsel Robert Mueller’s office last week disputing a bombshell news report that claimed Trump told Cohen to lie about the timing of discussions over a proposed Trump Tower project in Moscow.

“BuzzFeed’s description of specific statements to the Special Counsel’s Office, and characterization of documents and testimony obtained by this office, regarding Michael Cohen’s Congressional testimony are not accurate,” Peter Carr, a spokesman for Mueller’s office, said.

The statement is remarkable in that Mueller's team rarely issues statements in response to news stories. But BuzzFeed's story sparked immense interest from Democrats, who called for renewed investigations and even suggested the allegations could be a basis for impeachment proceedings.

Cohen in December was sentenced to three years in prison after pleading guilty to numerous crimes including campaign finance violations, tax evasion and lying to Congress about Trump’s past business dealings in Russia while cooperating with prosecutors.

Before sentencing, Cohen ripped into his former boss in federal court, telling the judge he felt it was his duty to cover up the president's “dirty deeds.”

Cohen is due to report to prison by March 6.

But Cohen has said he wants to use the opportunity of testifying before Congress to “give a full and credible account of the events which have transpired" working with Trump.

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The circumstances leading to the scheduled testimony have also come under scrutiny. Republicans on the House Oversight Committee claimed Tuesday that Davis orchestrated Cohen’s upcoming public hearing before the panel, and that Cohen was reluctant to do it.

Committee Ranking Member Jim Jordan, R-Ohio, and Rep. Mark Meadows, R-N.C., wrote a letter Tuesday to Cohen’s criminal defense attorney Guy Petrillo, requesting information ahead of Cohen’s appearance slated for Feb. 7. The letter includes extensive details, apparently based on a meeting with Davis, about his purported role in setting up what has become the most highly anticipated hearing of the new Congress.

"Davis made clear that Cohen's upcoming appearance before the Committee is entirely a result of Davis's orchestration," Jordan and Meadows wrote, questioning whether it's part of a broader "media stunt" to harm the president.

Fox News' John Roberts, Mike Emanuel and Brooke Singman contributed to this report.