Accused. Under investigation by the FBI. And still popular with Texas Republicans.

There were signals that Mr. Paxton’s long list of controversies tested the limits of Texas Republicans’ patience with him. Representative Chip Roy, a conservative who used to work for Mr. Paxton, called for his resignation in 2020. Along with Mr. Bush, Mr. Paxton’s main rivals were Representative Louis Gomert, who turned down a secure East Texas seat to run against him and Eva Guzman, who resigned from the Texas Supreme Court to challenge him in the primary. .

During his campaign, Mr. Gohmert predicted that Mr. Paxton would face new federal indictment after winning the Republican nomination and losing the general election to a Democrat. If Mr. Paxton does win the nomination but is defeated in November, it would be the first devastating blow for Republicans: no Democrat has won a seat in Texas since 1994.

In the Democratic primary for Attorney General, Rochelle Garza, a civil rights lawyer from South Texas, won the most votes and is heading to the runoff. Her Democratic opponent remained unclear. Third-place finisher Lee Merritt, a civil rights attorney, said in a statement that he was not prepared to give way to runner-up Joe Jaworski, the former mayor of Galveston, because the military and other ballots were still counted. Ms Garza said she was confident the attorney general’s office could be changed from red to blue. In 2018, Mr. Paxton won re-election, narrowly defeating his opponent Justin Nelson by 3.56 percentage points.

Mr. Paxton brushes aside any speculation about a Democratic victory in the fall. “In this country, accusations don’t make you guilty,” he told Radio Lubbock.

Aides to Mr. Paxton said Texas Republicans were unconcerned by the accusations and controversy surrounding his office. They claimed responsibility for the attack on Mr. Gomert and Ms. Guzman in order to allow Mr. Bush to qualify for the second round. After Paxton’s campaign attacked Ms. Guzman in a TV ad in the final days leading up to the primary, she fell from 21 percent of the vote in the early voting period to just 14 percent on Tuesday.

“This ad clearly cost Eve a runoff spot,” Dick Weekley, senior chairman of the Republican mainstream group Texans for Judicial Reform, which backed Ms. Guzman, wrote in an email to supporters after the primary.

Both Mr. Paxton and Mr. Bush will certainly continue to position themselves as true Trump supporters among Texas Republicans.