Federal regulators are tightening their oversight of car crashes that involve advanced driver-assistance or automated-driving features, a shift that follows growing concern over the role that systems such as Tesla Inc.’s Autopilot have had in crashes.

The National Highway Traffic Safety Administration said in a new order on Tuesday that companies must report serious crashes involving driver-assistance and automated-driving systems to authorities within a day of learning about them. Manufacturers and operators will also have to issue broader monthly reports about their vehicles’ safety.

“Gathering data will help instill public confidence that the federal government is closely overseeing the safety of automated vehicles,” NHTSA Acting Administrator Steven Cliff said.

The data will help investigators track patterns in automated-driving crashes, the agency said.

The order applies to simpler driver-assistance features that are already relatively commonplace, as well as more automated systems that are just beginning to gain wider adoption. The technology under scrutiny includes lane-keeping assistance and cruise-control systems that keep a fixed distance behind a leading car, as well as higher-tech systems such as features offered by Tesla that can guide a car along highways with minimal driver input.

Tesla didn’t immediately respond to an inquiry.

Potential safety issues with the systems include sensor failures and faulty decisions by software algorithms, NHTSA said in the order.

Fully self-driving cars, such as those being developed by Alphabet Inc.’s Waymo, would also fall under the order’s purview, the administration said. Waymo operates a ride-hailing service in the Phoenix area using autonomous minivans, and other developers have been testing self-driving cars on public roads in various cities.

NHTSA, which regulates auto makers, has looked into more than two dozen accidents involving Tesla vehicles, including several this year. One, a fatal Texas crash in April, happened without Autopilot engaged, Tesla Chief Executive Elon Musk said on Twitter.

That accident followed three other nonfatal Tesla crashes in February and March that also drew federal probes.

Earlier

Tesla CEO Elon Musk said data recovered so far from a fatal crash in Houston showed the car’s Autopilot system was “not enabled.” Local authorities believe the Tesla Model S was operating with nobody in the driver’s seat when it hit a tree. Photo: Scott J. Engle via Reuters (Video from 4/20/21) The Wall Street Journal Interactive Edition

After the Texas accident, Sen. Richard Blumenthal of Connecticut and Sen. Ed Markey of Massachusetts urged NHTSA to add to its oversight.

The National Transportation Safety Board, which issues safety recommendations, has also encouraged NHTSA to do more to ensure that driver-assistance features are safe.

Tesla has issued quarterly reports on vehicle safety since 2018. The company has used the reports to argue that its driver-assistance features help increase safety.

Last week, a safety issue with Tesla’s cruise-control system became the subject of a required software update affecting more than 285,000 vehicles in China, the company and Chinese regulators said.

Write to Matt Grossman at matt.grossman@wsj.com