The number of votes separating Representative Charles B. Rangel and his top challenger, State Senator Adriano Espaillat, shrank to 802 over the weekend, as the New York City Board of Elections released a new, unofficial vote count that for the first time included numbers from all precincts in the 13th Congressional District.

More than 2,000 absentee ballots and affidavit ballots — those cast by people whose names, for some reason, did not appear on the voter rolls — remain to be counted, a process that will not begin until Thursday morning.

In the meantime, Mr. Espaillat’s campaign, which is planning to go to court on Monday to ask that the ballots be secured, on Sunday hired Martin Connor, an election lawyer and former state senator, to lead its legal effort.

The Board of Elections released numbers on Saturday night based on data uploaded from memory sticks in each ballot scanner, showing Mr. Rangel received a total of 18,075 votes in the Democratic primary, or 44.29 percent of the votes cast, and Mr. Espaillat received 17,273 votes, or 42.33 percent.

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On Friday, Mr. Espaillat filed a petition in State Supreme Court in Manhattan against the Board of Elections, the New York Police Department, Mr. Rangel and three other candidates in the race, asking the court to supervise the canvassing process. The petition cited discrepancies in the reporting and counting of votes. It charged that, as of Friday, 6 percent of precincts in the district, many of them in areas where Mr. Espaillat was expected to do well, had not reported their vote totals.

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Justice Donna M. Mills ordered the parties to appear in her courtroom on Monday afternoon.

“We want to make sure that we have an opportunity to exercise every right every candidate has, to not only observe the canvassing of ballots but to protest or challenge ballots,” Mr. Connor said.