Representative Mike Collins, an immigration hard-liner, and Derek Dooley, a former college football coach and political newcomer, advanced Tuesday to a runoff in the Republican Senate primary in Georgia, according to The Associated Press.

The result moves the race to a June 16 showdown between two candidates with contrasting styles, backgrounds and pitches, if few clear policy differences. A third leading candidate, Representative Buddy Carter, a former pharmacy owner who brands himself as a “MAGA warrior,” was eliminated Tuesday, finishing third.

No candidate captured the majority of the votes required to clinch the nomination on Tuesday. With about 90 percent of the vote tallied early Wednesday morning, Mr. Collins was the leader, with Mr. Dooley running about 10 percentage points behind him.

The Republicans have battled for the chance to take on Senator Jon Ossoff, a first-term Democrat who is seen by his party as a rising star and by Republicans as a formidable adversary. Mr. Ossoff did not face a primary challenger on Tuesday.

Mr. Dooley’s showing extends the candidacy of a political newcomer backed aggressively by Gov. Brian Kemp, the state’s departing two-term governor and a lifelong friend of Mr. Dooley. Mr. Kemp campaigned with Mr. Dooley for weeks leading up to the primary on Tuesday, and the governor’s political organization directed millions of dollars to support the candidate.

As the race has played out, some in the party have grown anxious that they are poorly positioned for what is expected to be one of the most competitive Senate general elections in November.

The result on Tuesday did not appear likely to allay those fears. It sets in motion a monthlong runoff race that could bruise the finalists and drain resources that otherwise could be used in the general election.

Mr. Collins and Mr. Dooley have both put electability arguments at the core of their pitches to primary voters.

“We’re not here tonight because I’ve been propped up by somebody else,” Mr. Collins told supporters at his election night party in Jackson, Ga., on Tuesday. “No. We’re here because we work hard. We’ve got the best organization, the best voting record and the best message. And that’s what it’s going to take to beat Jon Ossoff.”

Mr. Dooley argued at his election night party in Atlanta that Mr. Ossoff would hammer Mr. Collins over a House ethics inquiry the congressman faces. (It relates to allegations that an intern for Mr. Collins’s congressional office had a relationship with a staff member and received pay without doing work. Mr. Collins has dismissed the matter, saying that the complaint is “bogus.”)

“We already got a preview of what the playbook is going to be for Jon Ossoff if Mike Collins is the nominee,” Mr. Dooley told supporters. “Jon Ossoff is going to take all that money he’s got from all over the state, and he’s going to put his Red Lobster bib on and go to work.”

Attacks between the candidates had already begun to sharpen in the final days before Tuesday’s primary. In one statement, Mr. Collins’s campaign called Mr. Dooley a “failed and fired Tennessee coach.” (Mr. Dooley led the University of Tennessee to three straight losing seasons in a three-year tenure from 2010 to 2012.)

Both runoff candidates have pushed for President Trump’s backing: Mr. Collins sponsored the first piece of legislation Mr. Trump signed after returning to office, the Laken Riley Act, a law targeting undocumented immigrants for deportation. Mr. Dooley met with the president at the White House for more than an hour in August, discussing sports and politics, according to his campaign. It is unclear if the president will weigh in before the runoff.

Instead of turning on the judgment of the president, the primary race has increasingly become a test of Mr. Kemp’s influence as he prepares to leave office.

Mr. Kemp says that Mr. Dooley is the only candidate in the race who can appeal to enough swing voters to have a chance of winning in November. Mr. Dooley is running as a political outsider and says voters are hungry for figures from beyond Washington. He has acknowledged he once went years without voting.

But the intervention by Mr. Kemp carries risks in the primary; the governor has had a tumultuous relationship with Mr. Trump ever since he refused to join the president’s efforts to reverse the 2020 presidential election.

Mr. Collins suggested at his election night party that while he had spoken to Mr. Trump about his race, he was leaving any decision about an endorsement to the president.

Mr. Collins has long leaned into a persona as a conservative brawler: Supporters at his election night party held signs saying “Georgia’s Conservative Workhorse.” And he has a history of incendiary social-media posts, including one suggesting that President Joseph R. Biden Jr. “sent the orders” for an assassination attempt against Mr. Trump in 2024.

But on Tuesday, he sought to cast himself as a candidate who could appeal to swing voters as well as the Republican base. In an interview at his election night party, he said that Georgia voters “just want somebody to go to Washington and do something for them.”

“Bipartisan to them is not a bad word,” he said. “And it shouldn’t be.”