Defying a wave of Republican victories across the nation, U.S. Representative Tim Bishop of Southampton, a Democrat, appears to have narrowly won his fifth term of office on Tuesday, marking the end of a bitter race that was watched nationally for its implications on the makeup of Congress for the next two years.

With all of the election districts reported as of early Wednesday morning, unofficial results from the Suffolk County Board of Elections show that Mr. Bishop defeated his Republican opponent, Randy Altschuler, by a margin of only about 3,500 votes. Mr. Bishop won 51 percent of the vote, to Mr. Altschuler’s 49 percent, and came just short of declaring victory in an early morning speech to scores of supporters who packed into the ballroom of the Marriott Hotel in Islandia.

“Well, it was a little closer than I would have liked,” said Mr. Bishop, 60, as he began his speech, shortly before 1 a.m., as the crowd cheered. “But I like where I am, and I’d rather be here than where he is.”

More than 9,500 absentee ballots are still outstanding, according to the Board of Elections. For Mr. Altschuler to pull off a last-minute win, he would have to take about 6,500 of those ballots, or approximately 68 percent. While mathematically possible, that would be a stunning turnaround: absentee ballots usually break in roughly the same proportions as the Election Day ballots, according to Ivan Young, assistant to Anita S. Katz, the Democratic commissioner of the Suffolk County Board of Elections.

The final results of the election, including absentee ballots, could take weeks to count, Mr. Young said.

Mr. Altschuler did not concede after the last unofficial results came in early Wednesday morning. He left Watermill Caterers in Smithtown and headed to his campaign office shortly before 1 a.m., after briefly thanking his supporters. “I am so overwhelmed by their dedication,” Mr. Altschuler said before heading to his office.

“We don’t have enough information to decide what to do,” said Rob Ryan, Mr. Altschuler’s spokesman. “We’re going to speak with an election lawyer to figure out the next step.”

Mr. Ryan said he heard reports that there were some problems with the new voting machines, forcing election workers to count some ballots by hand.

Mr. Altschuler, 39, a business owner from St. James, poured more than $2.7 million of his own money into the race and gave Mr. Bishop the most credible challenge of his eight-year political career. Still, it appears that he fell short in his attempt to wrest the 1st Congressional District seat from the incumbent. Just two years ago, Mr. Bishop trounced his Republican opponent, Lee Zeldin, winning by a margin of 58 percent to 42 percent. Mr. Zeldin won a seat in the State Senate on Tuesday.

Mr. Bishop faced a storm of challenges this election cycle, on top of his usual task of running as a Democrat in a district that traditionally leans Republican. Mr. Altschuler outspent Mr. Bishop by a wide margin, and the political atmosphere across the nation was treacherous for incumbents and Democrats. Republicans won control of the U.S. House of Representatives from Democrats on Tuesday, meaning that Mr. Bishop will be working in a new political environment in Washington, D.C.

In a testament to the tightness and importance of the race, former President Bill Clinton stumped for Mr. Bishop during a “get out the vote” rally at Stony Brook University in late October, less than one week before Election Day. A poll by the Siena Research Institute released on October 13 showed Mr. Bishop with a 12 percentage point lead over Mr. Altschuler, although the results on Election Day were much closer.

Audrey Kubetin, Mr. Bishop’s press secretary, said campaign efforts in recent days centered mostly on getting supporters to the polls. She said campaign staffers and volunteers knocked on almost 85,000 doors and made more than 88,000 phone calls since Saturday. “This thing comes down to turnout, and we’ve been working really hard to make sure our supporters get out and vote, get out of the house,” she said.

According to the Suffolk County Board of Elections, 42.24 percent of registered voters cast ballots in the congressional race—less than two years ago, a year when the presidential race brought in more voters, but in line with other off-year congressional votes.

Throughout Tuesday evening and into the early hours of Wednesday morning, a crowd of Mr. Bishop’s supporters gathered at the Marriott Hotel in Islandia to watch the results come in on a large screen. The race remained tight for hours, and the atmosphere in the room remained tense.

When Mr. Bishop finally took the podium, he thanked his family and staff, and said it was “hard to be ebullient” when so many other Democrats lost their seats on both the local and national stages. “What we have to do is dig in and fight back,” he said.