Republicans ended that probe in March, concluding there was no evidence of conspiracy or collusion between Russian Federation and Trump's presidential campaign.
Congressman Adam Schiff outlined a five-point plan for the committee's investigation, encompassing everything from Russia's election interference to the question of whether foreign governments have leverage over Trump, his relatives or associates.
A day after the Republican president warned Democrats against "ridiculous partisan investigations" in his annual State of the Union address, Schiff said they would not be intimidated.
Cohen was also scheduled to speak to the House Oversight and Reform Committee this week but pulled out, citing threats from Trump and the president's attorney-spokesman, Rudy Giuliani. Cohen pleaded guilty in November to lying to the House and Senate intelligence committees about his role in a Trump business proposal in Moscow.
The new Democrat-controlled House Intelligence Committee met for the first time Wednesday and wasted no time in making some moves. But Schiff said Wednesday morning that the interview had been postponed to February 28 "in the interests of the investigation".
The Intelligence panel previously agreed to send Mueller the closed-door testimony of Roger Stone, a long-time confidant of Trump.
Iraqi president hits back at Pres. Trump over US army presence
Former Iraq Prime Minister Haider Al-Abadi chimed in as well, writing on Twitter: "Iraqi sovereignty must be respected". Trump initially said the withdrawal from Syria should be immediate but he has since said it would be gradual.
Trump has repeatedly called the Justice Department investigation a "witch hunt" and insists there was no collusion. Stone is also charged with obstructing the House probe by encouraging one of his associates, NY radio host Randy Credico, to refuse to testify before the House panel in an effort to hide Stone's false statements. Mueller could potentially use these transcripts to pursue charges of perjury. It is possible that Mueller could have gained access to the documents through the intelligence agencies that are reviewing them.
It is unclear if Mueller has since requested any other transcripts, or if he has already seen any of them.
To protect ongoing investigative interests and information that remains classified, the Committee will release transcripts in a manner and according to a timetable that allows continued pursuit of important leads and testimony, while ensuring that the American people have faith in the process and can assess for themselves the evidence that has been uncovered, while legitimate national security interests continue to be protected.
Among the transcripts are interviews with Trump's eldest son, Donald Trump Jr.; his son-in-law, Jared Kushner; his longtime spokeswoman, Hope Hicks; and his former bodyguard Keith Schiller.
The committee will also investigate whether any of the president's policy decisions were the result of foreign exploitation and whether any foreign actors are attempting to impede congressional or other investigations into those topics.
Democrats also opposed a Republican motion at the meeting Wednesday to subpoena several witnesses.