Singh was found shot by other officers and taken to a hospital, where he was pronounced dead, police said.
The officer, identified as 33-year-old Ronil Singh, was a native of Fiji who immigrated to the United States to become a police officer and rose to the rank of corporal, authorities said.
"The type of tone and attitude that Sheriff Christianson has taken instills fear and panic in all immigrant communities" that could make people afraid to report crimes, de Leon said.
"He doesn't belong here, he is a criminal", Christianson said during a press conference Thursday while they were still searching for Arriaga. Ronil Singh was arrested.
Christianson says Perez Arriaga is from Mexico and was trying to cross back over the border before his arrest.
Talking about the suspect, Sheriff Christianson said that Arriaga was arrested twice previously for driving under the influence of alcohol and has known gang affiliation.
Gustavo Perez Arriaga was captured Friday after a manhunt following Singh's killing Wednesday.More news: Trump threatens to 'entirely' close US-Mexico border unless wall demands met
He was shot a few minutes after radioing that he was pulling over a grey pickup truck that had no license plate in Newman, a town of about 10,000 people, officials said.
Seven other people have been arrested on suspicion of helping Perez Arriaga, including his girlfriend and two of his brothers.
"My experience in NY has been different, where members of the NYPD-clearly the most professional, highly trained law enforcement entity in the country, if not the world-has been that these sanctuary laws actually help promote public safety by encouraging cooperation, encouraging communication between community and police in a way that allows police to better do their job", Jeffries said.
"This is a criminal illegal alien with prior criminal activity that should have been reported to ICE", Christianson said.
The shooting and manhunt in California's agricultural Central Valley entered the national debate over immigration, after Mr. Trump tweeted about it in his advocacy for a border wall and Mr. Christianson criticised California's sanctuary law.
In the past, the president has invoked the case of Kate Steinle to justify his attempts to withhold federal assistance to sanctuary cities.
Ahead of the congressional elections in November, a TV campaign ad endorsed by Trump focused on an undocumented Mexican immigrant convicted of killing two sheriff's deputies in California. Officials pleaded for help from the public and said they were following up on several leads.
This article was written by Michael Brice-Saddler, a reporter for The Washington Post.