Senior leaders from the Federal Aviation Administration defended the certification of the 737 Max at a Senate hearing on Wednesday, but raised the possibility of changing the process for approving new aircraft.

“We continue to hear of more problems with F.A.A.’s certification of the 737 Max aircraft,” Senator Susan Collins, Republican of Maine, said in her opening statement at a Senate Appropriations Committee hearing on oversight of the agency.

“These stories are particularly damaging for the leadership of F.A.A.’s safety oversight,” she added.

Since two crashes, in March and October, of Boeing’s 737 Max planes killed 346 people, lawmakers and federal investigators have been reviewing potential flaws in the agency’s approval of the plane. The F.A.A., which took longer than international regulators to ground the plane after the first accident, has come under fire for failing to catch the risks in new software on the Max that contributed to both crashes. The hearing covered a variety of aviation matters, but committee members took a specific interest in new reports of missteps in the Max’s certification.