Washington (CNN) President Donald Trump's former lawyer Michael Cohen and the Russian-born business associate he worked on the Trump Tower Moscow project with will both be returning to Capitol Hill next month to testify before the House Intelligence Committee, which is ramping up its probe of the proposed project.

Cohen was interviewed for more than seven hours behind closed doors before the House Intelligence Committee on Thursday, and the committee's chairman, Democrat Adam Schiff of California, announced Cohen would be returning on Wednesday next week to finish his testimony.

In addition, Schiff said that the committee would hold a hearing in public on March 14 with Felix Sater , the Russian-born onetime business associate of Trump's who worked on the Moscow Trump Tower project with Cohen. Schiff said that the committee "is going to try to do as much as we can in the open" with Sater.

Cohen's scheduled return, on March 6, is the date he was originally supposed to report to prison to begin serving a three-year sentence. A judge allowed his report date to be delayed two months, in part due to a request from Cohen's attorney to give him time to prepare for his congressional testimony.

Thursday's developments come on the heels of blockbuster public testimony from Cohen, delivered in a televised hearing of the House Oversight Committee on Wednesday. During that hearing, Cohen harshly criticized the President and accused him of directing the crimes Cohen committed, while Trump's GOP allies worked to counter his criticisms and undermine his credibility, in part by pointing to the fact that he has pleaded guilty to previously lying to Congress about how long discussions of a Trump Tower project in Moscow extended into the 2016 campaign.

Cohen spoke on a range of subjects involving his dealings with Trump during his public testimony, from what Cohen described as Trump's involvement in hush-money payments to women to his knowledge of longtime confidant Roger Stone's efforts to contact WikiLeaks.

Cohen's appearance before the House Intelligence Committee will be a much quieter event due to the fact that it will take place behind closed doors. The session is expected to focus on topics related to the panel's investigation into Russia's interference in the 2016 presidential election and ties between Russia and Trump associates.

The White House has joined with Republican allies in attacking Cohen's credibility and dismissing what he has to say amid his testimony on the Hill. The White House said ahead of Tuesday's closed-door hearing that it was "laughable that anyone would take a convicted liar like Cohen at his word."

Schiff told CNN before Thursday's testimony that his committee would "drill down" on a number of the topics that came up during Wednesday's hearing, as well as ask about a "number that were not raised." The California Democrat didn't specify but said the House Intelligence Committee would be "doing a lot of the painstaking work of identifying the source's corroboration."

Asked if he believes Trump had committed crimes, Schiff said that the Southern District of New York implicated him. "What we saw (Wednesday) was those crimes continued while he was in the Oval Office," Schiff said on the public hearing.

Intelligence Committee lawmakers said they expected the closed-door interview to last most of the day Thursday, after Cohen testified for roughly nine hours on Tuesday and more than seven hours on Wednesday.

Rep. Mike Conaway, a senior Republican on the committee, said Cohen had laid out areas he would not discuss in Thursday's interview, though Conaway would not elaborate on specifics.

The White House has joined with Republican allies in attacking Cohen's credibility and dismissing what he has to say amid his testimony on the Hill. The White House said ahead of Tuesday's closed-door hearing that it was "laughable that anyone would take a convicted liar like Cohen at his word."

Republicans took their charges against Cohen a step further Thursday, when Republican Reps. Jim Jordan of Ohio and Mark Meadows of North Carolina sent the Justice Department a criminal referral of Cohen for possible prosecution , claiming to have evidence that Cohen committed perjury in his testimony.

Meadows and Jordan, the top Republican on the Oversight Committee, urged the Justice Department to investigate Cohen's statements Wednesday that he did not seek a job in the Trump White House , his denial of committing bank fraud, as well as his assertion that the did not have any reportable contracts with foreign entities.

Democrats on the Oversight Committee have dismissed Republican accusations that Cohen lied. Rep. Jamie Raskin of Maryland told CNN Thursday morning that the line of questioning from his Republican colleagues was an "irrelevant distraction."

CNN has reached out to Cohen's attorneys and the Justice Department for comment.

Cohen's Capitol Hill testimony may be one of the last chances that lawmakers and the public have to hear from the President's ally turned adversary before he reports to prison.

Cohen is scheduled to begin a three-year prison sentence on May 6, a date that was pushed back by two months in part because his lawyer requested more time for Cohen to prepare for his congressional testimony.

He was sentenced in December for tax crimes, campaign finance violations tied to hush money payments to women and lying to Congress during his 2017 testimony about how long negotiations for a Trump Tower Moscow extended into the 2016 campaign.

Earlier in the week, Cohen appeared before the Senate Intelligence Committee for another closed-door session, testifying for roughly nine hours on Tuesday.

The main event, however, came on Wednesday with Cohen's public testimony before the House Oversight Committee.

In a fiery televised hearing, Cohen called Trump "a racist," "a conman" and "a cheat." He alleged that Trump had knowledge of Stone's efforts to reach out to WikiLeaks ahead of the release of hacked Democratic emails during the 2016 campaign and discussed Trump's alleged involvement in hush-money payments to women. Cohen told the committee that there was "no doubt in his mind" that Trump knew he was paying Cohen for "hush money payments."

Cohen provided new details claiming Trump was heavily involved in the pursuit of the Trump Tower Moscow project in 2016.

"To be clear, Mr. Trump knew of and directed the Trump Tower negotiations throughout the campaign and lied about it," Cohen said. "He lied about it because he never expected to win the election. He also lied about it because he stood to make hundreds of millions of dollars on the Moscow real estate project."

Cohen said that Trump did not "directly" tell him to lie to Congress, but that Trump would tell him personally and the public that he had "no business" with Russia, even as he was negotiating the Moscow project.

"In his way, he was telling me to lie," Cohen said.

This story has been updated with additional developments Thursday.