NATCHEZ — Forced into a Mississippi runoff, challenger Chris McDaniel and veteran Sen. Thad Cochran plunged into a three-week campaign Wednesday to pick a Republican candidate for the fall and settle the tea party’s last, best attempt of the year to topple a pillar of the establishment.

McDaniel, a narrow leader in the vote tally, spent the day resting with his family and “gearing up for what will hopefully be three more weeks of vigorous debate on the important issues facing Mississippians,” said spokesman Noel Fritsch.

Cochran, seeking a seventh term, skipped votes in the Senate during the day. He and his allies sought to put the best face on a relatively weak showing at the ballot box after three decades in office spent directing federal funds to his economically distressed state.

“We had a great day yesterday, and it is one more step toward making November Mississippi’s moment when we take back the U.S. Senate,” Cochran said in a written statement.

Yet there were indications of concern among supporters of the 76-year-old Senate veteran. Asked about Cochran’s prospects, fellow Mississippi Republican Sen. Roger Wicker paused at length before responding to reporters, “What do you think?” He then predicted Cochran’s victory in the runoff and said he would give the party its best chance to “hold the seat for a Republican majority.”

The third candidate in the race, real estate agent Tom Carey, said in an interview he had a preference between Cochran and McDaniel but declined to disclose it.

“The two candidates need to talk about issues instead of the backbiting and backstabbing that they’ve done,” Carey said, referring to the legal and political controversy that came when four supporters of McDaniel were arrested and charged in an alleged plot to illegally photograph Cochran’s wife, who has dementia and lives in a nursing home.

Results from 99 percent of the state’s precincts showed McDaniel with 155,040 votes, or 49.5 percent. Cochran had 153,654, or 49 percent. Carey had 4,789 votes, or 1.5 percent, a sliver of support, but enough to prevent either of the two better-funded rivals from reaching the needed majority.

Adams County voters favored Cochran, with the longtime senator receiving 54.69 percent of the vote.

Adams County Election Commissioner Larry Gardner said neither the Democratic or Republican parties can certify the local election results because of seven affidavit ballots that were cast.

The results will likely be certified Tuesday, Gardner said. The voters who cast the affidavit ballots did not have proper photo ID and have five days to present identification.

The runoff election is scheduled for June 24. Polls will again be open from 7 a.m. until 7 p.m., and voting locations will remain the same.

Voters who did not vote in Tuesday’s primary election can vote in the runoff.

If a resident voted in the Democratic primary Tuesday, he or she cannot vote in the runoff.

Voters must again present an acceptable photo ID to vote.

The Associated Press contributed to this report.