The victims' identities have not been confirmed by authorities, although they have been named by friends.
"Our hearts go out to the families and friends of the young people who lost their lives so tragically Saturday morning. Our thoughts are also with the young woman who survived and her family and friends, as this is an especially painful time for them," Gabel-Luddy said in the statement. "A tragedy of this magnitude affects the entire community, particularly one as close knit as Burbank."
On Saturday night, after dousing the fire, emergency personnel discovered five charred bodies inside the vehicle, police said.
At the vigil Sunday night, friends and family told KTLA-TV that the victims were all in their teens and early 20s and had graduated from Burbank high schools. Notes and candles lined the crash site as dozens of people gathered to offer condolences and share their grief.
Due to the young age of the victims, Gabel-Ludy also said it was important that "we pay close attention to their peers as they navigate the grieving process."
"The entire Burbank community feels the grief over this accident and we stand ready to assist. Burbank is a resilient community whose strength will help all of us to weather this trying time."
The cause of the crash remains under investigation. Anyone with information about the accident was asked to call Det. Sam Anderson at (818) 238-3100.