New York City public advocate Bill de Blasio has pulled further ahead in the New York City mayoral race, coming close to the 40 percent threshold he’d need to avoid a runoff in the Democratic primary, according to a poll released Wednesday by Quinnipiac University.

De Blasio took 36 percent among likely Democratic primary voters, by far the largest share of the vote any candidate has garnered in polling so far. New York City Council Speaker Christine Quinn and former city comptroller Bill Thompson trailed at 21 and 20 percent, respectively. Three other candidates, former Rep. Anthony Weiner (D-N.Y.), city comptroller John Liu and former city councilmember Sal Albanese, each polled in the single digits.

If there is a runoff, de Blasio would lead Quinn, 59 percent to 30 percent, and Thompson, 52 percent to 36 percent.