As he concluded his appearance before the House Intelligence Committee - one of three congressional hearings he had this week - Cohen told reporters he has another closed-door session with the same panel set for March 6.
In a public hearing before a House hearing on Wednesday, Cohen also attacked Trump's character, calling him a con man and a racist and voicing deep regret for working by his side for more than a decade.
Cohen, Trump's former personal attorney, said he was in Trump's office in July 2016 when Roger Stone was on speaker phone talking about WikiLeaks and its plan to publicly release hacked emails damaging to Democratic presidential candidate Hillary Clinton.
And Cohen asserted that lawyers for Trump and his family reviewed and edited his written testimony to Congress in 2017 in which he lied about the Moscow real estate deal.
Cohen said Howard, the executive editor of the Enquirer, was personally involved in co-ordinating "catch-and-kill" payments to two women who said they had affairs with Trump.
Talking to Hannity on Thursday, Trump pinned the blame on his former attorney for the payment scheme, even though a recording obtained by CNN past year reveals Trump discussing the payments with Cohen. The president described his former attorney and fixer's descriptions of him as "incorrect" and said the "fake hearing" was "shameful".
Cleveland Browns interested in trading for Antonio Brown
Head coach Kyle Shanahan and general manager John Lynch are in Indianapolis this week for the NFL Scouting Combine. He would not reveal, however, whether the Patriots had contacted him about a trade for Brown.
Democrats invited Cohen to testify after he started cooperating with Special Counsel Robert Mueller's Russian Federation investigation. Tweeted Scott, "Michael Cohen asked.no, BEGGED me REPEATEDLY, to ask the POTUS to give him a job in the Administration!"
Cohen testified that Weisselberg told him he'd be reimbursed for the payment in 12 monthly installments totalling $420,000, which included a bonus and covered some of Cohen's taxes and other work he'd done for Trump.
In addition to Special Counsel Robert Mueller and other federal prosecutors, several USA congressional committees are pursuing investigations focusing on President Donald Trump, looking at questions regarding Russia's role in the 2016 presidential election as well as the Republican president's finances.
He said prosecutors in NY were investigating conversations Mr Trump or his advisers had with him after his office and hotel room were raided by the Federal Bureau of Investigation last April. The drama was amplified by challenges from Trump's allies, including Rep. Jim Jordan, R-Ohio, that Cohen misrepresented his past in an effort to clean up his public image.
Trump Jr testified to the Senate intelligence committee that he was only "peripherally aware" of the project, while Ivanka said in an interview earlier this month she knew "literally nearly nothing" about it.
Without directly mentioning Cohen's specific comments about the alleged conversation, Stone said Cohen's "statement is not true". Ms James is already suing Mr Trump over what her office called "persistently illegal conduct" at the Donald J. Trump Foundation, which Mr Trump ran for 30 years. It has also subpoenaed the committee that raised $107 million to stage Trump's inaugural events.
During the hearing, Cohen accused Trump of being an unscrupulous person who cared only about winning but also contradicted himself by saying Trump never expected to win the presidency and just wanted to promote his brand. "I will not sit back, say nothing and allow him to do the same to the country".