HOUSTON — The Democratic challenger trying to unseat Representative Will Hurd, a two-term Republican congressman in the Texas border region, conceded the race on Monday, ending a nearly two-week dispute over the counting of provisional and other ballots in a tight race and sealing Mr. Hurd’s re-election.

Mr. Hurd’s majority-Hispanic district has been a hard-fought battleground for Democrats and Republicans. The 23rd District spans a wide swath of Far West Texas, including parts of San Antonio and some smaller border towns. The seat has flipped five times between Republicans and Democrats since the early 1990s, and Democrats were eager to make it six.

As it turned out, the race was so close that it took days of ballot examinations to determine the outcome.

[Read: A look at races still not called in the Nov. 6 midterm elections.]

Mr. Hurd and his opponent, Gina Ortiz Jones, a former Air Force intelligence officer, finished the election with one of the tightest vote margins in the state. Mr. Hurd had received 49.2 percent of the vote and Ms. Jones got 48.6 percent, with 1,150 votes separating the two candidates, according to state elections officials.