David Calone and Anna Throne-Holst, the candidates in the Democratic primary in the 1st congressional district, girded Wednesday for a paper ballot count, with only 29 votes separating them after Tuesday’s vote.

Throne-Holst, a former Southampton Town supervisor, leads venture capitalist Calone 5,446 to 5,417 votes, according to unofficial returns from the Suffolk County Board of Elections.

Both campaigns said it was too close to declare victory, while expressing confidence that uncounted absentee ballots would break their way.

The elections board had received 1,725 absentee ballots as of Wednesday, and will count any other ballots it receives by July 5, provided they were postmarked by June 27.

The count will begin late next week, and is expected to take several days, county officials said. Attorneys from the campaigns are expected to monitor the vote.

The campaigns said they had reached out to all 4,118 voters who requested absentee ballots to try to win their votes.

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Also, the Throne-Holst campaign made an appeal this month to supporters with homes in Manhattan, reminding them that they could change their voter registration to Suffolk County and request an absentee ballot.

“We feel very confident about the results tonight,” Throne-Holst campaign spokesman Andrew Grunwald said Tuesday night.

Calone spokesman Rahul Kale said the close margin in the race highlighted Calone’s grass roots support — the type of hard-core voters, he said, who request absentee ballots.

“I’m confident that voters who chose to vote absentee wanted to nominate the best candidate to defeat Lee Zeldin in November. And I’m confident that was Dave Calone,” Kale said.

Throne-Holst won six of eight towns covered by the district, unofficial results show. Calone of Setauket, ran up a 634-vote margin in his hometown of Brookhaven and a 123-vote lead in East Hampton, where he had the support of a majority of the town board.

The Board of Elections has not disclosed the towns of absentee voters.

The campaigns expect to establish legal defense funds. That would allow Calone and Throne-Holst to raise additional money from donors who have contributed the maximum of $2,700 for the primary campaign.

Zeldin, who defeated six-term incumbent Rep. Tim Bishop (D-Southampton) in 2014, on Wednesday released a 3-1/2 minute video touting his record serving in the U.S. Army in Iraq and homeland security legislation.

National Democrats have said that the district, which includes Brookhaven, Southampton, Riverhead, Southold, East Hampton, Shelter Island and slices of Islip and Smithtown, represents one of their best opportunities to defeat a sitting Republican. Nonpartisan election watchers have called the race a tossup.

Turnout in Tuesday’s Democratic primary was 9.22 percent, including absentee ballots, according to county election records.