Mr. Jeffries was leading Mr. Barron by a significant margin with just under half of all precincts reporting, according to the A.P.

Both men were running to replace Representative Edolphus Towns, who is retiring, in a newly redrawn district in Brooklyn. Mr. Barron, who has courted controversy with incendiary remarks during his political career, earned the endorsements of Mr. Towns and a major public employees’ union, alarming some Democratic leaders that he could score an upset victory.