The safety agency’s investigation will look at all models of Teslas — Y, X, S and 3 — from the 2014 to 2021 model years, totaling 765,000 cars, a large majority of the vehicles the company has made in the United States.

The new investigation comes on top of reviews the safety agency is conducting of more than two dozen crashes involving Autopilot. The agency has said eight of those crashes resulted in a total of 10 deaths. Those investigations are meant to delve into the details of individual cases to provide data and insights that the agency and automakers can use to improve safety or identify problem areas.

Tesla has acknowledged that Autopilot can sometimes fail to recognize stopped emergency vehicles. And safety experts, videos posted on social media and Tesla drivers themselves have documented a variety of weaknesses of Autopilot.

In some accidents involving the system, drivers of Teslas have been found asleep at the wheel or were awake but distracted or disengaged. A California man was arrested in May after leaving the driver’s seat of his Tesla while it was on Autopilot; he was sitting in the back of his car as it crossed the San Francisco-Oakland Bay Bridge.

At least one person died in one of the 11 crashes with emergency vehicles that are under investigation by the agency. Just days after Christmas in 2019, Derrick and Jenna Monet were driving on Interstate 70 in Indiana west of Indianapolis when their Tesla slammed into a parked fire truck, the Indiana State Police said at the time. Mrs. Monet, who was 23 years old and a passenger in the Tesla Model 3, died. Mr. Monet, who was driving the car, could not be reached for comment.