Gov. Larry Rhoden of South Dakota beat back a primary challenge on Tuesday and clinched the Republican nomination for a full term, The Associated Press said. The result positioned him as the strong favorite in November’s general election.

Mr. Rhoden, a rancher, ascended to his position from lieutenant governor last year when Kristi Noem left South Dakota to join President Trump’s cabinet. Mr. Rhoden faced an uphill fight to keep his post, competing in a primary that included the state’s sitting congressman, the speaker of the State House of Representatives and a businessman, Toby Doeden.

Mr. Doeden finished first in the opening round of balloting last month, with several thousand more votes than Mr. Rhoden. But he was short of the 35 percent threshold needed to clinch the nomination without a runoff. President Trump did not endorse a candidate.

Mr. Rhoden ran without some of the traditional advantages of the incumbency after succeeding Ms. Noem, who was the first woman to serve as South Dakota’s governor. Ms. Noem was fired as secretary of homeland security in March after a tumultuous tenure.

Mr. Rhoden, whose political style is more reserved than Ms. Noem’s, sought to forge his own political brand as governor. He announced the return of Fourth of July fireworks at Mount Rushmore, which Mr. Trump attended, and took on some of the state’s most pressing issues, including a long-stalled plan to build a new prison.

“I stay true to my planks of openness, civility and responsiveness,” Mr. Rhoden said in a debate hosted by KELO-TV, a station in Sioux Falls.

Mr. Doeden, who has several business ventures, stressed his status as a political outsider and sought to point out parallels he said he sees between his life story and Mr. Trump’s. On his campaign website, he pledged to be “the fiercest ally to President Trump in the nation.” He also called for reducing and eventually eliminating the state’s property tax.

“I will be the most pro-business governor this state has ever seen,” Mr. Doeden said in a debate hosted by South Dakota Public Broadcasting.

Mr. Rhoden will enter the general election as the clear favorite. No Democrat has held the South Dakota governorship since the 1970s. And with the exception of a tight race for governor in 2018, Democrats have shown few signs of electoral strength in the state in recent years.

Dan Ahlers, a former state legislator, will run on the Democratic Party’s ticket in November.