WASHINGTON — The head of the Federal Aviation Administration said on Wednesday that his agency had made mistakes in its handling of the crashes of two Boeing 737 Max jets and that the planes, which remain grounded, would not fly again this year.

Facing sharp questioning at a House Transportation Committee hearing, the F.A.A.’s administrator, Stephen Dickson, said the agency should have grounded the Max after the first deadly crash, in October 2018.

But his attempt to defend the F.A.A. was complicated by the release of an F.A.A. analysis, presented at the hearing, of that Lion Air accident off the coast of Indonesia. The analysis determined that the Max was likely to crash again if regulators did not act.

A second plane crashed under similar circumstances five months later, leading to the grounding of the Max and throwing Boeing into the worst crisis in its history.