The city "is joining the family and the community's call for justice, and we do support a full investigation into his death. We will settle for nothing less than a thorough accounting of this matter," the statement said.
Palmdale officials have reached out to Fuller's family, offering help and support, said John Mlynar, a spokesman for the city.
Fuller was pronounced dead by personnel from a nearby fire station who responded to the scene.
On Saturday, family, friends and community members gathered at a park in front of City Hall and held an emotional rally, demanding answers into Fuller's death.
"Although the investigation is on-going, it appears Mr. Fuller, tragically, committed suicide," the Sheriff's Department said in a Friday news release.
Hours later, at a well-attended Palmdale City Council Meeting, City Manager J.J. Murphy said there were "a lot of unanswered questions" in the case.
"We can't speculate, OK," he told attendees. "So my commitment to you, and our city's commitment to you, and the Sheriff's Department's commitment to you is: When we have more information, we will be 100% transparent."
On Saturday, Los Angeles County Supervisor Kathryn Barger released a statement requesting an investigation by State Attorney General Xavier Becerra into the death of Fuller.
The statement said, in part:
"Today, I asked California State Attorney General Xavier Becerra to conduct an independent investigation into the death of Mr. Robert Fuller who was discovered hanging from a tree in the City of Palmdale. The Attorney General, as the lead attorney and law enforcement official for the State of California, will lend additional expertise and oversight into this important investigation and provide the community with the answers they deserve."
An autopsy was conducted Friday by the Los Angeles County coroner's office, which deferred the cause of death.
"When a cause of death is deferred, a deputy medical examiner is requesting additional investigation, including laboratory testing and witness statements, before providing a final determination on the cause and manner of death,'' a coroner's spokesperson said.
Sheriff's Capt. Ron Shaffer said homicide detectives were investigating the circumstances leading to Fuller's death to determine if foul play was involved. He urged members of the public to contact detectives if they have relevant information, particularly about where Fuller had been and who he had been with in recent weeks.
Several celebrities took to social media and urged people to sign a Change.org petition demanding "security footage in Poncitlán Square to be presented and audio of the call placed when his body was found." The petition had more than 147,000 signatures as of Saturday afternoon.
If you or someone you know needs help, do not hesitate to call the National Suicide Prevention Lifeline at (800) 273-8255.