Congresswomen Nanette Diaz Barragan and Maxine Waters issued a joint statement asking Attorney General Xavier Becerra to conduct a full investigation into the shooting.
"Andres Guardado is the latest young man of color killed by police gunfire. He was shot in the back. The officers involved did not wear body cameras," the statement reads. "We demand answers and call for an independent investigation into this tragic death. There must be full transparency so the public can trust the investigation and we know we are getting the truth."
Los Angeles County Supervisor Mark Ridley-Thomas also issued a statement in support of an independent investigation by the Office of Inspector General.
During a press briefing on Saturday, the L.A. County Sheriff's Department said it is thoroughly investigating the shooting of Guardado as deputies spotted him with a gun and he ran.
Guardado's family is also demanding an independent investigation and maintains that the gun retrieved at the scene of the shooting was not his.
Capt. Kent Wegener, the head of the department's Homicide Bureau, said that investigators have taken six or seven exterior cameras from the scene of Thursday's shooting. Two of the cameras had ports for memory cards but were empty.
A search warrant was obtained to gain access to any "web-based video or security footage from the third-party vendor who supplies the service at the scene," Wegener said.
The killing in an alley among businesses in the Gardena area was the second fatal shooting by Los Angeles County deputies this week.
Thursday's shooting took place after deputies spotted Guardado with a gun in front of a business in the 400 block of Redondo Beach Boulevard near Gardena.
Wegener said Guardado ran from the deputies after he saw them. The deputies saw that Guardado had a gun, he said.
The shooting took place in the back of the building, Wegener said. Guardado was shot in the torso, he said, adding that the medical examiner will perform an autopsy.
Guardado's gun appeared to have been pieced together from different parts, and it did not have a serial number, Wegener said. Investigators do not believe Guardado fired his gun.
Guardado's family says he was working in the area as a security guard, but Wegnener said he was too young to work as a state-licensed security guard at the business and did not have any uniform or badge to indicate him as such.
Sheriff Alex Villanueva said the shooting underscores why the department needs to get body cameras for all of its uniformed deputies as soon as possible. The department is currently soliciting bids for a company to provide the cameras.
The Associated Press contributed to this report.