Cohen adviser Lanny Davis said the decision was made on advice of Cohen's lawyers.
Wolf Blitzer asked if Democrats are going to subpoena Cohen to appear before the Oversight Committee. "He has other clients also, I assume, and he doesn't want to tell the truth for me or other of his clients".
Despite a report Tuesday night, the legal team member said Trump wasn't "apoplectic" about Giuliani's statement and ensuing cleanup.
President Donald Trump claims his former personal lawyer, Michael Cohen, is postponing public testimony to Congress because Cohen has been - in Trump's words - "threatened by the truth".
They say they believe Cohen has "legitimate concerns" for his safety and security in light of threats from the president and Trump lawyer Rudy Giuliani. "We will not let the President's tactics prevent Congress from fulfilling our constitutionally mandated oversight responsibilities", the lawmakers said in a statement.
Cohen had volunteered to testify before the congressional panel.
Trump changes course, will delay SOTU till shutdown over
But the White House maintains Pelosi never formally rescinded her invitation, and is, in essence, calling her bluff. Pelosi, in a January 16 letter to the president, urged Trump to postpone it or to give it in writing.
In a Fox News interview this month, and other forums, Trump also suggested he had damaging information on Cohen's father-in-law. Politico reports that Giuliani's comments to the Times about a tower in Moscow "enraged Trump" because it undermined his public statement.
"I was aware, I think most people were aware of the tweet, 'watch father-in-law, ' but it's one of a bundle of tweets that you get sick of looking at that the president issues multiple times a day", Barnicle said.
GOP Rep. Mark Meadows of North Carolina, who is on the Oversight Committee, defended Trump from Cohen's accusations that the president was threatening his family.
Cohen was sentenced to three years in prison in December for crimes including orchestrating hush payments to women in violation of campaign laws before the 2016 presidential election.
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".
Cummings said, though, that Cohen could testify even after that.
In addition to tax evasion and bank fraud, Michael Cohen pleaded guilty late previous year to lying to Congress. Cohen lied under oath when he told congressional investigators that Trump's efforts to build Trump Tower Moscow ceased in January 2016 - because, according to Cohen, they actually ceased in June 2016. California Rep. Adam Schiff is chairman of the House Intelligence Committee. Rep. Adam Schiff, a California Democrat who chairs the House Intelligence Committee had indicated that he is seeking Cohen's testimony on Russian Federation related matters in a closed session in the near future.