(CNN) President Donald Trump's former personal lawyer Michael Cohen has agreed to testify behind closed doors before the House Intelligence Committee next week -- and he's tentatively agreed to go through with his planned testimony before the House Oversight Committee, according to Cohen's new lawyer Michael Monico.

Cohen's Oversight Committee testimony is not yet finalized, but he's in discussions to appear on February 7, the date he was initially scheduled to publicly testify before he abruptly announced last week that he was postponing his appearance.

House Intelligence Chairman Adam Schiff, a California Democrat, announced Monday that Cohen had agreed to testify before the intelligence panel behind closed doors on February 8.

Cohen has also been subpoenaed by the Senate Intelligence Committee to appear behind closed doors on February 12, according to his attorney.

Monico said Cohen wants to cooperate with all of the congressional inquiries. But the former Trump attorney's appearances on Capitol Hill appeared to be off last week when he announced he was postponing due to "ongoing threats against his family" from Trump and the President's attorney, Rudy Giuliani.

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