Senator Mike Braun of Indiana won the Republican nomination for governor of his solidly conservative state, The Associated Press said on Tuesday, positioning him as the strong favorite in this fall’s general election.

Mr. Braun defeated several other candidates, including Lt. Gov. Suzanne Crouch, in the primary. Mr. Braun, who received the endorsement of former President Donald J. Trump, has presented himself as a fiscal conservative and has pledged to take a tough stance on crime.

Indiana’s current governor, Eric Holcomb, a Republican who has occasionally bucked the right wing of his party on public health and cultural issues during his tenure, was barred by term limits from seeking re-election.

Mr. Braun, a businessman and first-term senator, will face Jennifer McCormick, the former state superintendent of public instruction, in November. Ms. McCormick, who was unopposed in the Democratic primary, was elected to her prior position as a Republican but fell out of favor with that party.

Indiana was once politically competitive. Barack Obama carried the state in the 2008 presidential race, and Mr. Braun’s predecessor in the Senate, Joe Donnelly, was a Democrat. But Republicans have dominated elections in Indiana over the last decade. Mr. Trump carried the state by 16 percentage points in 2020.

Republicans have used their control of state government to outlaw abortion in almost all cases, to ban gender transition treatments for transgender minors and to impose “intellectual diversity” requirements on public universities. State leaders have also cut income taxes and worked to attract business investments.

Mr. Braun, a former state legislator, defeated two Republican congressmen in the 2018 Senate primary before beating Mr. Donnelly by six percentage points in the general election.

In early 2021, Mr. Braun indicated that he would object to the certification of Joseph R. Biden Jr.’s presidential election victories in contested states. But after Trump supporters stormed the U.S. Capitol that Jan. 6, Mr. Braun reversed course and voted to certify the results.

Mr. Braun’s decision not to seek a second Senate term leaves an open seat that Republicans are widely expected to hold in the chamber. Representative Jim Banks, a former chairman of the conservative Republican Study Committee, is running unopposed for his party’s nomination and will face the winner of the Democratic primary in November.