Matt Gonzalez, the chief attorney at the San Francisco public defender’s office, said Monday he would be “honored” if Mayor London Breed appointed him to replace his former boss Jeff Adachi, who died Friday.

Breed has not indicated whom she will choose to replace Adachi as public defender before the seat is filled in the Nov. 5 election. “Right now, the mayor is focused on honoring Jeff’s legacy and life and has not made a decision yet,” said Breed’s spokesman, Jeff Cretan.

The appointment, if made, would mark another high-profile political venture for Gonzalez, the former Board of Supervisors president who once ran for city mayor and district attorney and was Ralph Nader’s running mate in an independent presidential bid in 2008.

“I would be honored to be the public defender, but I’m going to work with whoever gets appointed to make a good transition and be supportive of them, and make sure the office operates as well as it can,” Gonzalez said.

For now, Gonzalez, 53, will remain in his role overseeing day-to-day operations. He spoke Monday morning as attorneys returned to work for the first time since Adachi’s death. Gonzalez said he has authority to sign off on significant decisions but will refrain from major actions until Breed selects a successor.

Meanwhile, police continued to investigate Adachi’s death at age 59. He suffered an apparent medical emergency Friday evening in a Telegraph Hill apartment. An unidentified woman he was with called 911, and Adachi was later pronounced dead at a hospital. Police officials said they do not suspect foul play.

Gonzalez said he would not speculate on what kind of a leader he would be at the office and whether he would have the same firebrand style as his late boss. Adachi was an outspoken voice for his clients, as well as a police-misconduct watchdog who took up activist issues outside the traditional realm of a public defender.

“Jeff was not doing it alone,” Gonzalez said. “It’s part of the tradition and culture in the office now.”

Attorneys throughout the criminal justice system have praised Gonzalez’s legal mind. As a city supervisor from 2001 to 2005, he led the board’s progressive faction before running for mayor in 2003. He narrowly lost to now-Gov. Gavin Newsom.

“His legacy will be the great 2003 political race. It was the hallmark election of the last 20 years,” said San Francisco political analyst David Latterman. “We’ve never seen a race that polarizing. It was the leftists against what was going to be the new wave.”

Gonzalez settled into his job at the public defender’s office in 2011. But he rocketed back into the spotlight while defending Jose Ines Garcia Zarate in the death of Kate Steinle, who was shot on Pier 14 in July 2015 while walking with her father.

Gonzalez won an acquittal on a murder charge, arguing that the shooting was an accident that happened after Garcia Zarate found the gun and fired a bullet that ricocheted off the pier.

As attorneys got back to work Monday, authorities offered no new information on the circumstances of Adachi’s death. Police searched the apartment at 46 Telegraph Place where Adachi lost consciousness on Friday, and officers returned to the home over the weekend after obtaining a search warrant, a source familiar with the investigation said.

The Chronicle requested dispatch records and the 911 call from the woman who had been with Adachi, but the request was denied by the Department of Emergency Management, which cited “an ongoing criminal investigation.”

It is not unusual for police to get involved after the death of a public official, but Gonzalez expressed frustration about how the death has been handled.

“It has been disappointing to hear — I’ve been told, I don’t know if it’s true — that the police or members of the department, who did not like Jeff, have been trying to spread rumors, trying to make the circumstances of his death more salacious and trying to suggest all kinds of misconduct,” he said. “I guess that’s what happens when you’ve been a fighter against them and battled them the way he did.”

Some details about Adachi’s death remain unknown, including the whereabouts of the woman he was with.

According to a preliminary report on the incident reviewed by The Chronicle, police interviewed a real estate agent, Susan Kurtz, who is a longtime friend of Adachi’s and sometimes stays at the apartment with the owner’s consent. She said she allowed Adachi to use the apartment — which is typically unoccupied — for a couple of days.

Police were told Adachi fell ill while having dinner with an unidentified woman in North Beach and that the two took an Uber to the Telegraph Hill apartment. The woman called 911 at 5:41 p.m. and told a dispatcher that Adachi had drunk two glasses of wine, had complained of a stomachache and had taken a pill before he fell unconscious and stopped breathing.

Paramedics rushed Adachi to California Pacific Medical Center’s Pacific Campus, where he was pronounced dead at 6:54 p.m., according to the city medical examiner.

Officials identified Adachi and notified police, who headed to the scene at 8:37 p.m., according to the report. As officers were on the way, they were called off by the medical examiner but proceeded anyway, the report states.

The report says Kurtz received a call from the woman who had been with Adachi roughly two minutes after the 911 call. The woman was hysterical and said “something was wrong with Jeff.” Kurtz drove to the apartment, where she found the woman crying, the report states. The woman had left by the time police arrived, and Kurtz said she did not provide contact information.

Gonzalez said he believes Adachi had a heart attack. He said he was told Adachi drank two glasses of wine and took an antacid pill shortly before losing consciousness.

He also said Adachi had recently seen a specialist about a nagging cough and was under tremendous stress after winning an acquittal in a murder case he took to trial personally.

“I understand the public has an interest in how an elected official dies, and there are some question marks about what exactly transpired,” Gonzalez said. “I think that if somebody in the city has a heart attack and emergency personnel get called out to render medical assistance, that’s really not a crime scene. There’s not a situation where the police are being called out.”

Police officials on Monday defended the department’s actions, saying police were asked to respond before a cancellation request by the medical examiner’s office.

“The officer and their supervisor determined it was appropriate to respond to the scene in the event there was evidence to safeguard and collect per department policy,” Sgt. Michael Andraychak, a San Francisco police spokesman, said Monday.

He added that the department is also investigating “allegations of improper conduct and the release” of the incident report.

San Francisco Chronicle staff writers Dominic Fracassa, Phil Matier and Matthias Gafni contributed to this report.

Evan Sernoffsky is a San Francisco Chronicle staff writer. Email: esernoffsky@sfchronicle.com Twitter: @evansernoffsky