As of Monday's count, González had just under 41% of the vote.
King County estimated only 3,000 ballots were on hand to be counted as of Monday afternoon.
The winner will replace Jenny Durkan who declined to seek reelection.
González released a statement Thursday afternoon, conceding the race: "With today’s ballot drop, it’s clear that Bruce Harrell will be the next Mayor of Seattle. Earlier, I called him to congratulate him on a hard-fought race and wished him much luck in his efforts to make progress on the challenges Seattle faces."
Harrell, who grew up in redlined city neighborhood, would be Seattle’s first Asian American and second Black mayor. He has strong backing from business and real estate executives.
"We’re going to bring Seattle back together," Harrell told supporters after initial results were posted.
Harrell has criticized his opponent for supporting the goal of cutting the Seattle Police Department’s budget in half during the racial justice protests inspired by Floyd’s death — a position she has since softened.
The department is down hundreds of officers due to retirements and resignations amid the talk of defunding, and Harrell has called for the hiring of more police, including some unarmed officers, as well as the appointment of a cabinet-level position to address rising gun violence in the city.
Harrell has courted voters frustrated with visible homelessness. He said he would keep parks clear of tent encampments while also increasing shelter space, and he has vaguely suggested that unhoused people who refuse services could face consequences.
A regional authority will begin overseeing much of Seattle’s response to homelessness next year.
González, the daughter of migrant farmworkers, would be the city’s first Latina mayor. She’s been endorsed by service-worker unions as well as environmental and urbanist groups.
González and other leftist candidates have said they want to tax large corporations to provide money for affordable housing. They would end forcible removals of homeless encampments when there isn’t enough shelter or housing for the residents; end single-family zoning that prevents the construction of affordable housing; and invest in alternatives to policing, prosecution and incarceration.
She told supporters Tuesday night that her campaign will wait for all of the votes to be counted.
"Tonight’s results, and the fact that the votes of so many of our voters, who tend to vote at the very end, have not been counted means we may not know until late in the week or next week who the next mayor will be. We respect every vote as equal regardless as to when it was cast and we will not prejudge the outcome.
Our campaign is grateful for the support of hundreds of diverse organizations and people coming together in an intersectional movement - labor unions and environmental groups; renters and working people; small business owners and child care providers; Black, Latino, and Indigenous people; people of all ages and our wonderful LGTBQ community We come together because we believe in Seattle and want to work together to create a city where every single one of us has a place and a seat at the table."
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The Associated Press contributed to this report.