EL PASO — Representative Will Hurd of Texas, the only black Republican in the House, announced Thursday that he would not seek re-election next year, adding to a wave of departures that has unsettled party leaders as they hope to reclaim the majority in 2020.

Mr. Hurd, who is also the only Republican to represent a district along the southwestern border, is the sixth House Republican and the third Texan in the past 10 days to announce retirement. After the 2020 election, Senator Tim Scott, Republican of South Carolina, will be the only black Republican incumbent in Congress.

“Two centuries ago, I would have been counted as three-fifths of a person, and today, I can say I’ve had the honor of serving three terms in Congress,” Mr. Hurd said Thursday in a statement. “I will keep fighting to remind people why I love America: that we are neither Republican nor Democrat nor independent.” He did not say what he planned to do next. Before serving in Congress, Mr. Hurd was an undercover C.I.A. officer.

His announcement on Thursday made clear that the Republicans’ path to reclaiming the majority in the House and diversifying their party’s membership was becoming increasingly difficult. Two of 13 female incumbents — Representatives Martha Roby of Alabama and Susan W. Brooks of Indiana, who is a leader in candidate recruitment — and a handful of moderates are not planning to run again.