President Trump's former personal attorney Michael Cohen told House investigators this week that staff for Intelligence Committee Chairman Adam Schiff, D-Calif., traveled to New York at least four times to meet with him for over 10 hours immediately before last month’s high-profile public testimony, according to two sources familiar with the matter -- as Republicans question whether the meetings amounted to coaching a witness.

The sources said the sessions covered a slew of topics addressed during the public hearing before the oversight committee -- including the National Enquirer’s “Catch and Kill” policy, American Media CEO David Pecker and the alleged undervaluing of President Trump's assets.

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But, Republicans have raised concerns with the sessions, with Ohio Rep. Mike Turner sending a letter to Cohen's team on Wednesday demanding answers.

Turner specifically asked for confirmation of Cohen’s contacts, if any, "with Democratic Members or Democratic staff of SSCI [Senate Select Committee on Intelligence], COR [House Committee on Oversight and Reform], or HPSCI [House Permanent Select Committee on Intelligence] prior to his appearances before House and Senate committees last week" -- as well as the lengths of such contacts, their locations and who exactly was involved.

"These questions are important for the public to understand whether or not they were watching witness testimony, a public hearing, or well-rehearsed theater," he wrote.

During last month’s seven-hour public hearing before the House Oversight Committee, Cohen hesitantly acknowledged, under questioning from Ohio GOP Rep. Jim Jordan, that he had spoken with Schiff "about topics that were going to be raised at the upcoming hearing."

But, he did not elaborate on the discussions, which Fox News is told extended significantly longer than the seven hours that the public hearing itself lasted.

One by one, during the dramatic hearing, Cohen fielded questions on precisely the same topics that the sources told Fox News he discussed with Schiff’s staff during the sit-downs in New York.

For example, in response to questioning from Rep. Carolyn Maloney, D-N.Y., Cohen discussed the purported practice of paying for the rights to news stories harmful to Trump, only to bury them.

"I was involved in several of these catch-and-kill episodes," Cohen told Maloney, "but these catch-and-kill scenarios existed between David Pecker and Mr. Trump long before I started working in 2007."

Cohen went on to testify that Pecker, whose company publishes the National Enquirer, had paid $30,000 to a former Trump World Tower doorman who alleged he had information about a supposed love child fathered by Trump. The former Trump fixer asserted that Trump was concerned also about the "treasure trove of documents" Pecker had that could implicate him.

Further, Cohen was asked by Rep. Alexandria Ocasio-Cortez, D-N.Y., "To your knowledge, did the president ever provide inflated assets to an insurance company?"

Cohen replied: "Yes."

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"Who else knows that the president did this?" Ocasio-Cortez pressed.

"Allen Weisselberg, Ron Lieberman and Matthew Calamari," Cohen said, referring to the Trump Organization's chief financial officer and other key Trump associates. "You deflate the value of the asset and then you put in a request to the tax department for a deduction."

Cohen also brought documents that he claimed proved Trump "inflated" his assets in order to obtain loans from Deutsche Bank.

Asked about the revelations by email, a House Intelligence Committee spokesman defended the Schiff staff's pre-hearing discussions with Cohen.

"We are running a professional investigation in search of the facts, and we welcome the opportunity to meet with potential witnesses in advance of any testimony to determine relevant topics to cover in order to make productive use of their time before the Committee," spokesman Patrick Boland told Fox News.

"Despite this professed outrage by Republicans, it’s completely appropriate to conduct proffer sessions and allow witnesses to review their prior testimony before the Committee interviews them — such sessions are a routine part of every serious investigation around the country, including congressional investigations."

Schiff was asked about the frequency of his contacts with Cohen on CBS News' "Face the Nation" this weekend, and gave the number "seven" -- but Schiff did not distinguish between the number of his own contacts with Cohen and the committee staff's interactions with him.

Schiff asserted, "The extent of my contact was just inviting him to testify and also trying to allay his concerns about the president's threats against him and his family ... but our staff certainly sat down to interview him, and that's what you do in any credible investigation."

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A source close to Schiff claimed some details about the staff meetings were “not accurate” but did not point to specifics.

On Cohen, a source familiar with his closed-door testimony before the House Intelligence Committee would not comment directly on the number and substance of the meetings between Cohen and the Schiff staff, but said more broadly that Schiff "pledged to release the full transcript of Mr. Cohen’s eight hour testimony, at which point Mr. Cohen will be vindicated and others will be implicated."