Sheriff, family grieve off-duty LA deputy's 'senseless and cowardly murder' The 13-year veteran was shot at a Jack in the Box on Monday.

A Los Angeles County deputy who was killed this week while off duty is being remembered as a kind-hearted family man who gave 13 years of "selfless service," the Los Angeles County sheriff said.

Deputy Joseph Gilbert Solano, 50, was shot while off-duty at a Jack in the Box in Alhambra on Monday afternoon, and died on Wednesday at the same hospital where he had last been assigned to work, said Sheriff Alex Villanueva.

"Deputy Solano was known as a kind-hearted and generous family man, a provider for his mother and an exemplary father to his children," Villanueva said. He called the slaying a "senseless and cowardly murder."

Villanueva was joined at a news conference on Wednesday with members of Solano's family, who at times were overcome with emotion.

"Thank you to everyone that has had him in his prayers," Solano's son, Matthew Solano, said. "Continue to pray for him and my family, please."

Deputy Solano's step-daughter, Jessica, said, "he has been in my life for over 11 years. And not only did I lose a father figure, but a best friend."

"Don’t forget about him," she said. "He was a hardworking man and was loved by many."

Rhett Nelson, a 30-year-old from Utah, was arrested on Tuesday as a suspect, after a revolver matching the gun used in the attack on Deputy Solano was found in Nelson's car, authorities said.

Clothing found in Nelson's car appeared to match the outfit seen on the gunman in surveillance video, authorities said.

The sheriff said there's no indication that the suspect knew Deputy Solano was a law enforcement officer.

"The deputy was alerted in the restaurant that someone was following him and that's when he turned to confront it," Villanueva said. "He confronted a threat not knowing what it was and in a split second he lost his life."

No motive is known, the sheriff said.

Meanwhile, Los Angeles Police Chief Michel Moore said that Nelson is also considered a suspect in the murder of a 30-year-old man in Los Angeles that occurred about one hour before Deputy Solano was shot.

San Diego authorities also said they're investigating if five armed robberies in the San Diego area over the weekend could be linked to Nelson.

It was not immediately clear if Nelson had an attorney. He is due to appear in court on Thursday.

ABC News' Alex Stone contributed to this report.