Lawyer Lanny Davis, who has been advising Cohen on his media strategy, says in a statement that Cohen had decided to postpone his appearance to a later date due to "ongoing threats against his family from Trump" and Trump's lawyer Rudy Giuliani, as well as his ongoing co-operation with investigators.

Trump called Cohen a "rat" in a tweet last month for co-operating with prosecutors.

Cohen had been Trump's self-described longtime "fixer" and once said he would take a bullet for the New York real estate developer.

In a Fox News interview this month, Trump suggested he had damaging information on Cohen's father-in-law.

"That's the one that people want to look at," Trump said in the interview.

Davis last week called Trump's comments intimidation.

"There is no question that his threatening and calling out his father-in-law, who - quote - has all the money, is not only improper and unseemly for a bully using the bully pulpit of the presidency, but the very definition of intimidation and witness tampering," Davis said.

Cohen did not immediately respond to a request for comment.

Giuliani also did not immediately respond to a request for comment.

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.

He said in the guilty plea that he was directed to make the payments by Trump.

Cohen had volunteered to testify before the House of Representatives Oversight Committee on February 7.

Davis said Cohen looked forward to testifying at a later date.

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

Australian Associated Press