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It was billed as a contest of criminal justice reformers, a six-way Democratic primary for district attorney in Queens that would soften the tough-on-crime policies that have long typified this working-class borough of New York.

Hours after the polls closed Tuesday, the race seemed too close to call, with Tiffany Cabán, a 31-year-old public defender , holding a narrow lead over Melinda Katz, the Queens borough president .

Ms. Cabán declared victory shortly after 11 p.m., telling the crowd at her watch party, “We did it y’all.” But Ms. Katz did not concede; speaking to her supporters just before 11 p.m., she said that every vote should be counted.

“God willing, I will come out on top,” she said.

With 99 percent of precincts reporting, Ms. Cabán led Ms. Katz by 1.3 percentage points . Roughly 3,400 absentee ballots have to be counted, with Ms. Cabán’s margin at roughly 1,100 votes. Board of Election officials said the count may not be completed until Wednesday, July 3.