Washington(CNN) Michael Cohen told lawmakers Wednesday that President Donald Trump suggested during a 2017 White House meeting that he hide from Congress how plans to build a Trump Tower in Moscow continued through much of the 2016 campaign.

Cohen also made new allegations about how Trump's personal lawyers reviewed his now-fraudulent congressional testimony about the proposed Trump Tower in Moscow and made "changes" to it before he testified, but he did not identify what those changes were.

"There were changes made, additions -- Jay Sekulow, for one," Cohen said Wednesday, referring to one of the President's personal attorneys. "There were several changes that were made including how we were going to handle that message, which was -- the message of course being -- the length of time that the Trump Tower Moscow project stayed and remained alive."

Cohen did not elaborate about the changes, who made them, or if they changed what Cohen admitted was already false testimony.

Sekulow responded to Cohen's claim in a statement to CNN, saying, "Today's testimony by Michael Cohen that attorneys for the President edited or changed his statement to Congress to alter the duration of the Trump Tower Moscow negotiations is completely false."

In wide-ranging testimony before the House Oversight Committee, Cohen described a meeting at the White House in May 2017, as he was preparing his now-false congressional testimony with Trump and Sekulow. Cohen said Trump made clear at that meeting what he wanted him to say.

"He doesn't tell you what he wants. What he does is again, 'Michael, there's no Russia, there's no collusion, there's no involvement, there's no interference.' I know what he means because I've been around him for so long," Cohen testified. "That's the message that he wanted to reinforce," he said.

Cohen added that his 2017 testimony was circulated among lawyers pursuant to a joint defense agreement to make sure attorney-client privilege was protected, which would be a normal part of the process, according to multiple sources.

Cohen said he created the document with his attorney at the time, Stephen Ryan, and circulated to other attorneys including Abbe Lowell, an attorney for Ivanka Trump and Jared Kushner, the President's daughter and son-in-law who are both White House advisers.

Cohen's now-former lawyer, Guy Petrillo, first raised the idea that others were involved in Cohen's testimony. In a court filing he wrote, Cohen "remained in close and regular contact with White House-based staff and legal counsel to (Trump)" while he prepared his false testimony. The court filing didn't identify any of the individuals. None of the sources who spoke to CNN on Friday could say if "White House-based staff" were consulted.

Rep. John Sarbanes, D-Maryland, later sought to clarify with Cohen who at the White House reviewed his testimony and Cohen said he didn't know. When asked what edits were made, Cohen answered he would need to look at the document to recall how it was edited. Asked if he reacted to the false testimony at the time, Cohen said, "No, sir because the goal was to stay on message. It's just limit the relationship whatsoever with Russia, it was short, there's no Russian contacts, there's no Russian collusion, there's no Russian deals. That's the message. That's the same message that existed well before my need to come and testify."

Cohen also drew a link between his 2017 false testimony and the review by Trump's attorneys in his written prepared remarks.

"Mr. Trump knew of and directed the Trump Moscow negotiations throughout the campaign and lied about it. And so I lied about it too -- because Mr. Trump had made clear to him through his personal statements to me that we both knew were false and through his lies to the country, that he wanted me to lie. And he made it clear to me because his personal attorneys reviewed my statement before I gave it to Congress," Cohen said.

Cohen pleaded guilty last year to lying to Congress about the duration of talks to build a Trump Tower in Moscow, saying they did not end in January 2016 before the Iowa caucus as he previously said but instead continued until June 2016 as Trump clinched the Republican nomination.

Several court filings relating to Cohen's guilty plea indicated that White House-based staff and a lawyer for Trump were aware of Cohen's testimony before he delivered it. In a filing made by special counsel Robert Mueller's office, the lawyers wrote that Cohen "described the circumstances of preparing and circulating his response to the congressional inquiries," suggesting there was some significance to the involvement. But none of the filings named any of the parties.

CNN has learned that the group of lawyers consulted in the preparation of Cohen's written congressional testimony included attorneys representing the President, members of his family and the Trump Organization.

Two of the sources familiar with the preparation, including one close to the Trump Organization and one close to the President's legal team, said the lawyers had no indication that any of the information in the testimony of Trump's now-former longtime attorney and fixer was inaccurate.

The lawyers who saw the draft testimony included: Alan Garten and Alan Futerfas, attorneys for the Trump Organization and its executive vice president, Donald Trump Jr.; Sekulow; and Lowell.

Mueller's team said in a court filing that Cohen provided "relevant and useful information" for their investigation and that Cohen "described the circumstances of preparing and circulating his response to the congressional inquiries."