Waymo is recalling software in thousands of its driverless taxis that could allow the vehicles to drive into flooded roadways, according to a letter from the National Highway Traffic Safety Administration.

The letter, dated Monday and posted to the administration’s website, concerns the automated driving systems in all 3,791 cars in the company’s fleet.

“The software may allow the vehicle to slow and then drive into standing water on higher speed roadways,” the regulatory body said in the letter. “Entering a flooded roadway can cause a loss of vehicle control, increasing the risk of a crash or injury,” it said.

Waymo said it decided to recall the software last month after an unoccupied car entered a flooded road during a heavy downpour in San Antonio on April 20. Even though the road was “untraversable,” the vehicle proceeded at a reduced speed, the safety agency noted in a report last week.

Chris Bonelli, a Waymo spokesman, said by email that the company — which is owned by Google’s parent, Alphabet — “provides over half a million trips every week in some of the most challenging driving environments across the U.S., and safety is our primary priority.”

Mr. Bonelli said Waymo had “identified an area of improvement” regarding flooded lanes on high-speed roadways.

“We are working to implement additional software safeguards and have put mitigations in place, including refining our extreme weather operations during periods of intense rain, limiting access to areas where flash flooding might occur,” he said.

According to Waymo, the software will be fixed without interrupting the taxi service, since it can be updated when the vehicles return to a depot for regular maintenance and recharging. Waymo has paused public service for rides in San Antonio, Mr. Bonelli said.

The recall is one in a string of incidents that have called into question the safety of self-driving cars as they proliferate across major American cities.

Waymo is facing federal investigations into traffic violations, and it issued a voluntary software recall in December after reports that its robotaxis had illegally passed stopped school buses. Its cars have also been involved in more serious incidents, including instances in which an ambulance was blocked from getting to the scene of a shooting in Austin, a cat was killed in San Francisco and a child was struck in Santa Monica, Calif.

While confronting these incidents and a general wariness of the autonomous technology, the company has been battling to earn the public’s trust. Waymo says its technology statistically outperforms humans, reducing the chance of crashes and the resulting serious injuries.