Minutes later, Torrance officers responding to a report of gunshots encountered another dark pickup matching the description of Dorner's, said Torrance Sgt. Chris Roosen. A collision occurred and the officers fired on the pickup.
The unidentified driver was not hit and police later realized they had made a mistake, Roosen said.
"We're asking our officers to be extraordinarily cautious just as we're asking the public to be extraordinarily cautious with this guy. He's already demonstrated he has a propensity for shooting innocent people," said Andrew Smith, the LAPD commander.
Dorner is wanted in the killings of Monica Quan, and her fiance, Keith Lawrence. They were found shot in their car at a parking structure at their condominium Sunday night in Irvine, authorities said.
Quan, 28, was an assistant women's basketball coach at Cal State Fullerton. Lawrence, 27, was a public safety officer at the University of Southern California. There was disbelief at three college campuses, Fullerton, USC, and Concordia University, where the two met when they were both students and basketball players.
On Thursday morning, Dorner's wallet and photo ID and a law enforcement badge were found on a street near San Diego International Airport.
Dorner was believed to be heavily armed and wearing military-style fatigues and body armor.
Mexican authorities closely watched San Diego's border with Tijuana and were prepared to shoot him in a confrontation, said Alfredo Arenas, international liaison for the Baja California state police.
The FBI and U.S. marshals provided constant updates.
"We're keeping tabs with them every five minutes to see if he comes to Tijuana," Arenas said. "If push comes to shove, they advised us to shoot to the head."
Arenas said the Mexican navy was also watching out.
Dorner is suspected of tying up an 81-year-old man and trying to steal his boat at the Southwestern Yacht Club in San Diego on Wednesday night. He fled when he couldn't start the engine.
The yacht club is about five miles from where Dorner's wallet was found, San Diego police said.
On Monday morning, authorities found Dorner's police equipment in a dumpster in the San Diego suburb of National City.
Associated Press writers Jeff Wilson and Robert Jablon in Los Angeles contributed to this report.