LOS ANGELES — The police in California’s Central Valley are hunting for a man who they believe killed a police officer and is in the country illegally, according to authorities.

The shooting occurred around 1 a.m. Wednesday, when Ronil Singh, a 33-year-old officer, was gunned down after pulling over a driver he suspected was drunk in east Newman, Calif., a town of about 10,000 people not far from Modesto. The case was soon thrust into the nation’s fractious debate over immigration when President Trump tweeted about it Thursday afternoon.

“There is a full scale manhunt going on in California for an illegal immigrant accused of shooting and killing a police officer during a traffic stop,” Mr. Trump wrote. “Time to get tough on Border Security. Build the Wall!”

Mr. Singh, officials said, was an immigrant himself, from Fiji, and had worked for the Newman Police Department since July 2011. He was married and had a 5-month-old son, and after spending Christmas morning with his family went on duty that night.