Kshama Sawant initially trailed incumbent Richard Conlin by more than 6,000 votes, but with Tuesday's vote update, now leads Conlin by 41 votes -- 79,751 to 79,710.
Sawant spoke about the newest vote tally at a Tuesday afternoon press conference.
"People believe in this change and they want this change to happen and they're willing to make a sacrifice to make it happen," she said.
The next count of ballots for elections in King County will be released at 4:30 p.m. Wednesday. More mail-in ballots may be counted before election results are certified Nov. 26.
Sawant is a former software engineer and economist who made a proposed $15 an hour minimum wage the centerpiece of her campaign.
Conlin is seeking his fifth term on the city council.
Council races in Seattle are non-partisan but, Sawant won a court decision to list her socialist preference on the November ballot.
"What we have shown here is that our ideas, socialist ideas, far from being French ideas, are exactly what people are looking for, and this is enormous," Sawant said.
Conlin wasn't available for comment on Tuesday.
The Seattle City Council race isn't the only one that's still too close to call. An initiative that seeks to establish a $15 minimum wage for many workers in SeaTac is still unresolved following Tuesday's vote tally.
On election night, the initiative jumped out to a 261-vote margin -- a decent gap in a race that's likely to draw maybe 6,000 total votes. Supporters declared victory but have since lost much of their advantage, with opponents gaining ground during each ballot drop.
As of Tuesday evening, the ballot measure was winning by just 43 votes.