Only about 20% of the building has been searched and "a significant number" of people are still missing, they said.
It is unclear what caused the fire at the converted warehouse.
The safety record of the building is under close scrutiny. There were no sprinklers. The only exit from the second floor was a makeshift stairwell.
Meanwhile, a man identified by former residents as the collective's co-operator, has drawn criticism for a Facebook post, in which he wrote that "everything I worked so hard for is gone", without acknowledging those who died.
Oakland fire chief Teresa Deloach-Reed said between 50 and 100 people were inside the venue when the fire started late on Friday.
The old warehouse, known as the Ghost Ship, was hosting a concert by electronic group Golden Donna and six other acts.
The fire caused the roof to collapse on to the second floor, part of which then fell through to the ground floor.
The building did not have a sprinkler system and firefighters did not hear any alarms when they arrived, Ms Deloach-Reed said.
The warehouse, which housed artists in improvised studios, was packed with furniture, mannequins and other objects, obstructing firefighters' efforts to put out the blaze, she added.
"It was filled end to end with furniture, whatnot, collections. It was like a maze, almost."
Fire crews worked all night at the scene. The search for bodies is expected to continue for at least another 48 hours.
Melinda Drayton, battalion chief at the Oakland Fire Department, said firefighters were going through the debris "bucket by bucket".
"It was quiet, it was heartbreaking," she said, choking back tears. "This will be a long and arduous process.
"We don't believe we have even gotten close to the origin of the fire."
She said every precaution was being taken to treat the victims' remains with respect.
Only three of the bereaved families are believed to have had their loved ones' deaths confirmed, due to issues with identification.
Oakland's Planning Department said it had opened an investigation into the premises last month after complaints from neighbours about rubbish, and of people living inside, against building regulations.
One former resident, Shelley Mack, told the Associated Press (AP) the building was "like a horror house", adding that there was no electricity or running water.
Media in Oakland named Derick Ion as the co-operator of the collective with his partner, Micah Allison.
A Facebook post by Derick Ion lamenting the loss of his belongings but saying he was "blessed that my children and Micah were at a hotel safe and sound" drew a barrage of criticism online.
Neither co-owner has commented publicly and their whereabouts are unknown.
Much of the work in the wake of the fire has focused on securing the building to allow search teams and investigators to enter.
Relatives of those who are missing have gathered at the Oakland coroners' office.
"I just want to go over there," Dan Vega, whose brother and his girlfriend are missing, told AP. "I have my work boots on. I'm ready to go."
Thirty bodies have so far been recovered from a warehouse in Oakland, California, following a deadly fire during a party, officials say.