Image copyright AP Image caption Mr Suhr - a veteran officer - was appointed city police chief in 2011

San Francisco's Police Chief Greg Suhr has stepped down hours after a police officer shot and killed a young black woman.

The resignation was announced by Mayor Ed Lee, who had asked him to quit.

The woman reportedly tried to drive off in a stolen car and ignored calls to stop in the Bayview area of the city.

Mr Suhr and city police have in recent months come under fierce criticism over fatal police shootings of several black suspects.

At a news conference on Thursday, Mayor Lee said: "A young woman of colour was killed in an officer-involved shooting in the Bayview (area). The community is grieving, and I join them in that grief."

Image copyright Reuters Image caption Earlier, protesters held a rally outside the city hall, demanding the sacking of Greg Suhr

The woman, 27, who has not been named, was reportedly sitting in a stolen car when a police patrol approached her.

She allegedly tried to drive off and then crashed into a nearby vehicle.

There was no immediate indication that she had a weapon or had tried to run down a police officer before the shooting, the city authorities said.

Racist messages

The San Francisco police department and its chief have recently come under fierce criticism over the death of several black suspects and reports that a number of officers had exchanged racist text messages.

In April, five people went on a hunger strike, demanding Mr Suhr be sacked. They ended their strike last week.

The mayor, who until now had supported Mr Suhr, added: "The progress we have made has been meaningful but it hasn't been fast enough, not for me and not for Greg, and that's why I have asked Chief Suhr for his resignation."

He named Toney Chaplin as acting police chief.

Image copyright AP Image caption The new Police Chief, Toney Chaplin, says the police's problems "are bigger than one man".

Analysis: BBC's David Willis in California

A 34-year veteran of the San Francisco PD, Greg Suhr was once a popular and professional policeman.

"Greg was always respectful, always a servant of the community," recalled London Breed, who first encountered Suhr when the latter was a young narcotics officer working the beat. Both would go on to greater things: Suhr to police chief, Breed to president of the local Board of Supervisors.

But for Suhr there were missteps along the way - among them a demotion from deputy chief after a female friend told him she had been assaulted by her boyfriend and he failed to file a police report.

Reflecting on Suhr's resignation, London Breed said she hoped the city would now come together so that everyone would feel safe in their communities.

The job of reforming the police department now rests with Greg Suhr's former deputy Toney Chaplin - another insider, with 26 years of service under his belt.

Mr Suhr, a veteran officer, was appointed city police chief in 2011.

There are more than 1,000 fatal shootings by police in the US each year, and those killed are disproportionately African-American.