Just hours after Chair James Comer (R-Ky.) rebuffed Bill and Hillary Clinton's attorney's last-ditch conditional offer, the former president and former secretary of state appear to have acquiesced and agreed to key demands from the Republican-led House Oversight Committee to testify about Jeffrey Epstein in a closed-door deposition.

The initial correspondence, obtained by CNN, revealed that the Clintons' team has been in search of an off-ramp for days.

Attorneys for Bill and Hillary have been in discussion with the Republican-led committee multiple times since lawmakers from both parties voted in January to hold the Clintons in contempt for refusing to appear for in-person depositions as part of the panel's investigation into Epstein.

"It has been nearly six months since your clients first received the Committee's subpoena, more than three months since the original date of their depositions, and nearly three weeks since they failed to appear for their depositions commensurate with the Committee's lawful subpoenas," Comer wrote.

"Your clients' desire for special treatment is both frustrating and an affront to the American people's desire for transparency."

As CNN reports, according to the letter dated January 31, the Clintons' lawyers laid out the terms under which the former president would sit for a voluntary, transcribed interview.

He would sit for four hours in New York City for an interview limited to the scope of the Epstein probe, they said.

Lawmakers from both parties and their staff could ask questions, and the lawyers said both the Clintons and the committee could have their own transcriber present, according to the letter.

Comer rejected the offer from the Clintons' attorneys as "unreasonable" and said he could not accept such terms.

He could not agree, he said, to changing the interview from a sworn deposition to a voluntary interview, and rejected the way in which the attorneys sought to limit the interview's scope. 

"But given that he has already failed to appear for a deposition and has refused for several months to provide the Committee with in-person testimony, the Committee cannot simply have faith that President Clinton will not refuse to answer questions at a transcribed interview, resulting in the Committee being right back where it is today," the Kentucky Republican wrote.