Kshama Sawant initially trailed incumbent Richard Conlin by more than 6,000 votes, but is now leading by about 40 votes -- 79,751 to 79,710.
The next count of ballots for elections in King County will be released at 4:30 on 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.
More Northwest Headlines
Court denies Medina millionaire’s release from Montana jail Anti-wildlife trafficking initiative qualifies for ballot 2 Yakima County men sentenced for killing eagles USGS awards $4M in Northwest, California for earthquake early warning systems Commuter train hits vehicle in Puyallup, kills 1 woman Ex-tribal police chief pleads guilty to stealing from Swinomish Tribe Hearing Friday on suit over Kurt Cobain death-scene photos Guilty plea in crash through Sammamish home that killed 2
Our new comment system is not supported in IE 7. Please upgrade your browser here.