The investigation is separate from the probe into Spalding's death being done by the San Francisco police and from the internal investigation of hospital security measures by the San Francisco Sheriff's Department.
"A thorough independent review is required, and we will do that," Lee said. "I will say this: The city is responsible for what happened here."
Lee, who was director of public works and city administrator for San Francisco before he was elected mayor, said that on Thursday he visited the floor where Spalding had been staying, both to comfort hospital staff members and to get a sense of the layout.
Lee said the hallway that runs from Spalding's room to the fire exit stairway passes elevators, a hallway leading to another wing and a number of doors. The area right by the door to the stairwell "seems a little bit isolated. You could turn the corner and nobody would see."
He said he opened the door to the stairwell and an alarm went off as it was supposed to, but that it may have been hard to hear elsewhere on the busy floor.
Spalding, who lived with her daughter in San Francisco, was taken to the hospital because she had lost weight and appeared disoriented and weak, and her family and friends were concerned about her physical state. She was admitted for a bladder or urinary tract infection on Sept. 19 and was reported missing from her room two days later.
Perry, the family spokesman, said Spalding's family welcomes the mayor's promise of a thorough investigation.
The Sheriff's Department provides security at the large, sprawling hospital and would have had primary responsibility for searching it once Spalding disappeared, he said. The San Francisco Police Department opened a missing person case on the day she went missing and fielded tips and followed leads elsewhere, he said.
"At this point, the real issue is not the reason she was in the hospital but how a search by the San Francisco Sheriff's Department failed to find her," Perry said. "Obviously a more thorough search should have been done if a woman's body was here for 17 days."
Perry says that Spalding's children are grieving deeply following the coroner's confirmation Wednesday night that the body in the stairwell belonged to their mother.
"It's one thing to hear your mom may be dead," Perry said. "It's another to hear your mom is dead."