The front-runner in Mississippi’s Republican primary election for governor was forced into a runoff on Tuesday by two rivals who have broken with Southern conservative orthodoxy to support Medicaid expansion under the Affordable Care Act.

The front-runner, Lt. Gov. Tate Reeves, is a believer in small government who opposes expanding the federal health care program in Mississippi.

But his primary challengers — William L. Waller Jr., a former chief justice of the State Supreme Court, and Robert Foster, a state representative — ran on a promise to expand government health care in one of the country’s reddest states. Mr. Waller also supports raising a gas tax to fix roads and bridges, an idea Mr. Reeves opposes.

The Associated Press declared early Wednesday morning that Mr. Reeves and Mr. Waller will face off in an Aug. 27 runoff. With 97 percent of precincts reporting, Mr. Reeves had 48.9 percent of the vote, less than the 50 percent needed to avoid a runoff. Mr. Waller had 33.4 percent of the vote, and Mr. Foster had 17.8 percent.