Breed, president of the Board of Supervisors, was leading Leno by fewer than 1,900 votes Tuesday with about 245,000 ballots tallied and at least 9,000 ballots left to count. Her lead has been increasing since Saturday.
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Exuberant and excited, she appeared before supporters and reporters on the steps of City Hall to say she was humbled, honored and looking forward to being the city's next mayor.
VIDEO: Here's how ranked-choice voting works
VIDEO: Here's how ranked-choice voting works
She said she was thrilled at the message her election sends to San Francisco's youth, especially impoverished kids growing up like she did.
"No matter where you come from, no matter what you decide to do in life, you can do anything you want to do," she said. "Never let your circumstances determine your outcome in life."
The elections office was set to release an updated tally at 4 p.m. Wednesday.
Earlier in the day Mark Leno told reporters crammed into his tiny print shop that he had a positive conversation and that Breed was gracious.
VIDEO: Mark Leno concedes after close SF mayor's race
VIDEO: Mark Leno concedes after close SF mayor's race
"She is a remarkable young woman and she is going to do a very fine job. Her success is San Francisco's success," he said.
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Leno, 66, did not rule out a future run for office. In his remarks, he thanked fellow candidates, especially Supervisor Jane Kim, who joined with him in pushing a more liberal agenda. And he thanked voters for exceeding low turnout expectations.
Turnout exceeded 50 percent, which is higher than usual for recent June gubernatorial primaries and mayoral elections.
"This was a campaign about change, a campaign about the betterment of the great city of San Francisco," he said.
San Francisco is remarkably wealthy thanks to an economy boosted by the tech sector, but it also has deep pockets of poverty and an entrenched problem with homelessness.
MEET THE CANDIDATES: London Breed
Meet San Francisco mayoral candidate London Breed
Despite a compelling personal story that showed her as an underdog, Breed was the favorite of the business and political establishment communities going into the contest. Mayor Ed Lee died in December, setting off a race that was not supposed to occur until next year.
Breed raised the most money of the three leading candidates with the help of big contributions from big backers, at least $2.3 million to her political campaign committee and two other committees that supported her.
She faced spirited opposition from Leno and Kim, who said that Breed represented the status quo that had made San Francisco so inequitable. All three are Democrats.
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The portrayals of her as a lackey bugged Breed.
"I ask people to not attribute what I've done -my success and how hard I've worked- to not reduce that or attribute that to someone else," Breed told the AP in a pre-election interview.
MEET THE CANDIDATES: Mark Leno
Meet San Francisco mayoral candidate Mark Leno
The former executive director of the African American Art & Culture Complex grew up in the historically black Western Addition, raised by her grandmother in public housing. They drank powdered milk and ate meat from a can labeled "pork," she said.
Breed consistently maintained her lead in first-place votes, but San Francisco uses a unique ranked-choice voting system that allows voters to pick their top three for mayor.
Breed has 50.42 percent of the vote, including nearly 37 percent of first-place votes.
Breed will have to run in the November 2019 election for a four-year term.
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