The Cohen's adviser went on saying that that former Trump's personal lawyer would testify "at the appropriate time".
Trump, when asked Wednesday to respond to Cohen's accusation that his family has been threatened by the president and his attorney, Rudy Giuliani, said Cohen was not threatened by him, but is "threatened by the truth".
"In order to get his sentence reduced, he says, I have an idea, I'll give you some information on the president". Cohen says he lied to minimize the public understanding of Trump's Russian Federation ties, to try to limit the various Russian Federation investigations and to be consistent with Trump's "political messaging". "And he doesn't want to do that, probably for me or other of his clients".
Cohen's testimony is set to be the first major public hearing for Democrats, who have promised greater scrutiny of Mr Trump. He pleaded guilty to campaign finance violations related to the payments.
There has been great interest in Cohen's testimony.
It wasn't immediately clear whether "threats" cited by Cohen's camp were the only reason he decided not to appear at Cummings' hearing next month or whether Mueller's office might have objected.
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"We understand that Mr. Cohen's wife and other family members fear for their safety after these attacks, and we have repeatedly offered our assistance to work with law enforcement to enhance security measures for Mr. Cohen and his family".
President Donald Trump is not angry at his attorney Rudy Giuliani, despite the former NY mayor's contradictory answers in recent interviews about a proposed Trump Tower project in Moscow, sources told CNN Tuesday - and Giuliani is not going anywhere. "That's the money in the family".
As the president continued to engage in what Cohen sees as reckless and unsubstantiated claims he believes are meant to intimidate him, Cohen had expressed to friends his concern that Trump's heated rhetoric on television and Twitter could incite an unstable person to target him or his family. Cohen also played a pivotal role in buying the silence of a porn actress and a former Playboy Playmate who both alleged they had sex with Trump. "Mr. Cohen's statement is long on conclusions and short on facts and details", said Boutros, a former federal prosecutor. Committee chair Elijah Cummings could subpoena Cohen to appear, and CNN reports Democrats are considering that option. California Rep. Adam Schiff is chairman of the House Intelligence Committee.
In a letter to Cohen attorney Guy Petrillo, Reps. Giuliani said he knows that Trump did not counsel Cohen to lie because he listened to the tapes.
Cohen's decision raised the possibility that the committee would issue a subpoena compelling him to testify.
The Senate committee did not immediately confirm the subpoena, but any interview with Cohen would nearly certainly take place in private, in keeping with how the panel generally conducts Russia-related hearings.