Five weeks after a runoff, a Cruz-backed House candidate concedes defeat in Texas.

Five weeks after a too-close-to-call Republican primary runoff in a Southwest Texas congressional district, Raul Reyes, a retired Air Force colonel, has abandoned a recount and conceded defeat to Tony Gonzales, a former Navy cryptologist, by a handful of votes.

Texans viewed the 23rd District’s House race as a referendum on the popularity of President Trump, who had backed Mr. Gonzales, versus Senator Ted Cruz, who had endorsed Mr. Reyes.

A mere seven votes separated Mr. Gonzales and Mr. Reyes on Election Day, July 14, with the vote count 12,346 to 12,339. After absentee and overseas ballots were counted in the 29-county district, Mr. Gonzales’s lead had grown to 45 votes.

Mr. Reyes demanded a recount, hoping that would put him ahead. But he said late Friday that a review of votes in the larger counties in the sprawling and rural district had netted him only six additional votes, reducing Mr. Gonzales’s margin of victory to 39 votes. As a result, he said, he concluded that it would be impossible to pick up those 39 votes in the remaining rural counties.