The former White House chief of staff during then-President Donald Trump's administration, Mark Meadows, said on Tuesday that he will stop cooperating with the House select committee investigation on the January 6 Capitol riot.

The select committee threatened to recommend criminal contempt charges if he fails to appear for a testimony, according to a CBS News report.

Meadows said that despite their cooperation in sharing documents with the select committee, they had issued a subpoena to a third-party carrier trying to get information, unknowingly to them. The former chief of staff said that they feel it is best that they continue to honor the executive privilege, adding that it is looking like the courts are going to weigh in on it.

The select committee heads Reps. Bennie Thompson and Liz Cheney said that they still have questions about the documents Meadows submitted.

In a joint statement, the House select committee will be left with no choice but to file contempt proceedings and recommend him for a criminal prosecution, according to an Axios report.

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Mark Meadows and House Select Committee

George Terwilliger, Meadows' attorney, said that the parties had reached an understanding of how to exchange information. He noted that he made efforts over many weeks to reach an accommodation with the committee.

Terwilliger said that Meadows believed he would not be answering questions he said were protected by executive privilege. However, the select committee had implied that it wanted to address such matters, describing the acts of the select committee made an appearance "untenable."

Terwilliger further noted that the select committee has no intention of respecting boundaries surrounding executive privilege.

Meanwhile, the select committee heads argue that Meadows was refusing cooperation while openly talking about details of the incident in his book.

The former chief of staff's lawyer said that Thompson publicly said that another witness's claiming of the fifth amendment would be equal to an admission of guilt, which was a reference to a former justice department official, Jeffrey Clark.

Clark has been threatened with a charge of contempt of Congress if he does not cooperate with the investigation on incidents that occurred on January 6, according to The Guardian report.

On Tuesday, Meadows has released his book entitled "The Chief's Chief."

California Rep. Adam Schiff said that it was very possible that by discussing the event of January 6 in his book, Meadows is waiving any claim of privilege.

Thompson noted that part of what they plan to ask Meadows is in the excerpts of the book.

Meadows has refused to answer questions about whether he used a private mobile phone to conduct business that day, according to an Independent report.

He was also asked where are any email or text messages he sent or received on that phone are located.

On the other hand, Georgia Secretary of State Brad Raffensperger has told committee members that he received text messages from a private email account owned by the former White House chief of staff.

Legal experts noted that Meadows has no right to invoke the executive privilege as it is U.S. President Joe Biden who decides whether it can be used to shield documents or testimony.

Biden has declined to invoke the executive privilege.

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Written by: Mary Webber

WATCH: Meadows backtracks on Capitol riot probe - from Reuters