Tesla Inc. late Friday acknowledged its semiautonomous Autopilot system was engaged by the driver in the seconds before a fatal crash last week, raising more questions about the safety of self-driving technology on public roads.

Federal investigators this week began examining the March 23 crash of a Model X sport-utility vehicle that was traveling south on Highway 101, near Mountain View, Calif., before it struck a barrier, then was hit by two other vehicles and caught fire. The driver of the Model X was killed.

Tesla...