Former CIA Director David Petraeus agreed to testify before the House and Senate Intelligence committees on the Benghazi attack this week, despite his resignation from the agency over an extramarital affair.

Committee Chairwoman Dianne Feinstein (D-Calif.) said Wednesday that Petraeus would voluntarily come before the panel in a closed-door session to discuss the attack on the U.S. Consulate in Libya and noted that the hearing would not address his affair.

Petraeus will testify before the Senate committee either Thursday or Friday, Intelligence Vice Chairman Saxby Chambliss (R-Ga.) told The Hill, although the details were still being finalized early Wednesday evening.