Bass had been behind as of Thursday afternoon's figures. But on Friday, she was ahead of developer Rick Caruso by nearly 4,400 votes, putting the race - for now - at 50.38% in her favor, to Caruso's 49.62%.
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Bass had a total of 289,782 votes while Caruso had 285,398. Voter turnout for the race is estimated at 27%,
Getting definitive results to call the race could take some time - days or even weeks - as the registrar so far has tallied just 62% of the vote.
Friday's update represented an additional 79,018 ballots counted for all Los Angeles County races, for a total of just over 1.53 million. Of those countywide ballots, more than 29,000 were added specifically to the city mayoral race count.
The registrar's office still has more than 811,000 ballots left to count, though that number could increase as more ballots come in with a postmark of Election Day. It's not known how many of those 811,000 outstanding ballots countywide are specifically for city of Los Angeles races.
The registrar is expected to release additional results Saturday and Monday afternoons.
Both campaigns said they remain optimistic and are looking at planning a potential transition into office.
"In the coming days, the voice of the people of Los Angeles will be heard and we feel confident that we will win," Sarah Leonard Sheahan, Bass' communications director, said in a statement on the latest vote count. "As mayor, Karen Bass will chart a new direction for Los Angeles with comprehensive solutions for homelessness, public safety and affordability."
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In response to the latest numbers, Caruso's campaign in a statement said: "There are a lot of votes to count. We're cautiously optimistic about these numbers and looking forward to the next series of results. There is so much work to be done around homelessness and crime, we're eager to move forward."
In a tight mayor's race, the favorite is Bass, a former state Assembly leader who has the advantage of being a lifelong Democrat in a city where Republicans are almost invisible.
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She's backed by President Joe Biden and the Democratic establishment and has been promising to use her skills as a coalition builder to heal a wounded city.
Caruso campaigned on an abrupt change in direction, arguing that Bass and other longtime politicians are part of the problem that has led L.A. into multiple crises.
WATCH: LA mayoral hopefuls Karen Bass, Rick Caruso discuss crime and more
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Eyewitness Newsmakers: LA mayoral hopefuls Karen Bass, Rick Caruso discuss housing, crime, policing
He is promising to expand the police department to deal with rising crime rates and quickly get ubiquitous homeless encampments off the streets.
The winner will replace beleaguered Democrat Eric Garcetti, who will conclude two uneven terms with his nomination to become U.S. ambassador to India stalled in the Senate, apparently over sexual misconduct allegations against a former top Garcetti adviser.
The Associated Press and City News Service contributed to this report.