Jay Furman, a retired Navy officer, has won the Republican nomination to challenge embattled Representative Henry Cuellar of South Texas in November, according to The Associated Press.

Mr. Furman defeated his challenger, Lazaro Garza Jr., a rancher, in a runoff after the two emerged as the top vote-getters in a crowded March primary. Mr. Cuellar, a centrist Democrat, is still largely expected to win re-election in Texas’ 28th Congressional District. But the terrain has become somewhat more favorable for Republicans after Mr. Cuellar was indicted this month on federal bribery and money-laundering charges.

Mr. Cuellar and his wife, Imelda Cuellar, are accused of accepting at least $598,000 over seven years from a Mexican bank and an oil company owned by the government of Azerbaijan, according to the federal indictment. He has denied any wrongdoing.

In his district, which stretches from his hometown, Laredo, and the U.S. southern border to the eastern outskirts of San Antonio, Mr. Cuellar is considered an institution. He has powerful allies on both sides of the aisle and has survived two bruising Democratic primary contests. Even former President Donald J. Trump — who is on trial over allegations that he falsified business records — has come to his defense, arguing Mr. Cuellar became a target of the Biden administration because he supports tight border policies.

Mr. Cuellar’s fund-raising efforts have dwarfed those of his Republican opponent. At the end of March, Mr. Cuellar had raised nearly $2 million and had more than $415,000 cash on hand. As of May, Mr. Furman had raised just under $195,500 and had roughly $2,013 cash on hand, according to the latest federal filings for each campaign.

Still, Mr. Furman is betting the charges against Mr. Cuellar have improved his odds. The election forecasters Cook Political Report and Sabato’s Crystal Ball have both shifted their rating for the general election from likely Democratic to leans Democratic.

Mr. Furman, who grew up in Austin and lives in San Antonio, served in the military for nearly 30 years before returning to Texas. Like Mr. Garza, he has made immigration central to his campaign. He echoes Mr. Trump’s inflammatory rhetoric and calls for hard-line actions, including mass deportations. On his website, he also has promised to tackle inflation, empower small businesses and block “‘woke’ insanity.”

In an interview, Mr. Furman argued the charges against Mr. Cuellar were “exactly in line with what the people have come to expect of the Cuellar dynasty.” But he also echoed Mr. Trump in his criticism of the Justice Department, which he contended had been weaponized against conservatives.

“My goal is not only to highlight his charges,” he said, “but also the arbitrary capricious enforcement of the law by our Department of Justice.”