The shootings appear to have occurred after robberies or attempted robberies at the four convenience stores in the early hours of July 11, or 7/11 – the day the 7-Eleven brand is celebrating its 95th birthday in the US.

“Our hearts are with the victims and their loved ones,” 7-Eleven said in a statement.

“We are gathering information on this terrible tragedy and working with local law enforcement.”

It was not immediately clear to investigators what prompted the shootings in the cities of Riverside, Santa Ana, Brea and La Habra, or why the violence occurred on July 11.

“The only person to answer that would be the suspect,” Riverside Police Department spokesman Officer Ryan Railsback said. The first shooting happened in Riverside at about 1.50am.

“There’s no way it can be a coincidence of it being 7-Eleven, July 11.”

The Riverside shooting – where the victim was in grave condition – has not yet been officially connected to the others, Railsback said, “although they all seem very, very similar”.

“It doesn’t appear to be any reason that the suspect shot the customer,” Railsback said.

“It sounds like the clerk gave him whatever he asked for.”

In that case, the gunman robbed the clerk and brandished a gun, then turned the weapon on a customer, opened fire and fled, Railsback said.

The second shooting occurred about 3.20am, about 39 kilometres) away in Santa Ana, authorities said.

Officers responding to reported gunshots at the 7-Eleven in that city found a man dead in the parking lot with a bullet in his upper torso, according to Sergeant Maria Lopez, a Santa Ana police spokeswoman.

The violence appeared to include an attempted robbery.

“At this moment, we don’t believe he was an employee. We don’t really know yet what he was doing there in a parking lot, if he was a potential customer or just walking by,” Lopez said.

Lopez said detectives believe the suspect in the Santa Ana killing is the same person who then travelled 19km to Brea, where a 7-Eleven employee was found dead with a gunshot wound at about 4.18am.

Brea Police Captain Phil Rodriguez said officers responded to a report of a man suffering from a gunshot wound and found the employee wounded. He was later pronounced dead.

“This does appear to be a robbery that turned into a homicide,” Rodriguez said.

Less than an hour later, officers in neighbouring La Habra were sent to a reported robbery at a 7-Eleven. They discovered two gunshot victims about 4.55am, according to Sergeant Sumner Bohee. The gunman had fled.

“We feel confident that it is the same suspect,” Rodriguez said.