In a tedious exercise that could determine whether veteran Rep. Charlie Rangel keeps his seat, the New York City Board of Elections on Thursday began to count the roughly 2,000 remaining provisional and absentee ballots in the disputed primary between him and his top Democratic rival. 

The 13th Congressional District race appeared decided last week on election night, with Rangel seemingly holding a sizable lead. State Sen. Adriano Espaillat, his rival, even gave a concession speech. 

But the vote margin shrank, and Espaillat went on to claim he had received scores of complaints from residents claiming their votes had been suppressed. 

Now, the remaining uncounted ballots could determine the race. Board of Elections commissioners told Fox News they expect to wrap up their count by the weekend or early next week. 

At each table Thursday, a bipartisan team of four elections board employees -- two Democrats and two Republicans -- recorded the number of ballots that had already been validated by the elections board.