Updated

Battling for his political survival, six-term Mississippi Sen. Thad Cochran was declared the winner in a tight Republican runoff race Tuesday night -- but Tea Party-backed challenger Chris McDaniel has not outright conceded and his campaign is weighing whether to challenge the results.

The runoff was held after neither candidate clinched the GOP nomination in the June 3 primary, and Tuesday's election was every bit as competitive.

The Associated Press reported that unofficial returns showed Cochran, a 76-year-old first elected to Congress in 1972, with a lead of just over 6,000 votes, holding 50.8 percent of the vote to McDaniel's 49.2 percent with 99.9 percent of precincts reporting.

“It’s been a real pleasure working with so many of you and making appearances in towns all across Mississippi,” Cochran said during his brief victory speech late Tuesday night, in which he thanked those who had helped him secure what he called a "great victory."

"It's a group effort. It's not a solo. And so we all have a right to be proud of our state tonight," he said.

More On This...

    The runoff was to be a test of whether Cochran could win over voters with his Washington seniority and clout, against his Tea Party-backed challenger.

    But a defiant McDaniel, a state senator, offered no explicit concession when he spoke to his supporters in Hattiesburg, instead complaining of "dozens of irregularities" that he implied were due to Cochran courting Democrats and independents.

    "We are not prone to surrender, we Mississippians," McDaniel told his backers. "Before this race is over we have to be absolutely certain the Republican primary was won by Republican voters."

    Tea Party leaders told Fox News early Wednesday that McDaniel campaign operatives had been up all night weighing whether to challenge the results on the grounds that Democratic voters allegedly crossed over from the Democratic primary to vote for Cochran. Under Mississippi law, voters in one party's primary must intend to support that party's nominee in the general election.

    Of particular interest to the McDaniel campaign was the turnout in Hinds County, which Cochran won by nearly 11,000 votes Tuesday. By contrast, Cochran won the county by 5,300 votes on June 3. Just under 25,000 total ballots were cast in Hinds County Tuesday, while 16,640 total ballots were cast on June 3.

    Following the shocking ouster of House Majority Leader Eric Cantor in Virginia June 10, Tea Party groups focused their energy on the Mississippi race -- backing McDaniel -- as the next test of their own influence.

    The race attracted about $12 million in spending from outside groups. Former Green Bay Packers quarterback — and Gulfport, Mississippi, native — Brett Favre called the 76-year-old Cochran a "proven and respected leader" in one ad paid for by the U.S. Chamber of Commerce.

    Cochran and his allies, notably former Gov. Haley Barbour, promoted his Washington establishment credentials, focusing on the billions he funneled to his home state, one of the poorest in the nation. In a last-ditch effort, Cochran reached out to traditionally Democratic voters — blacks and union members — who could cast ballots in the runoff. That possible factor in Cochran's victory is sure to be cited by critics in days and weeks to come.

    In predominantly black neighborhoods of Hattiesburg's south side, an organized effort for Cochran was evident. Ronnie Wilson, a 50-year-old unemployed Hattiesburg man, said he had been encouraged by his pastor to vote for Cochran.

    "They say the other guy is trying to cut food stamps and all that," Wilson said. "I'm trying to look after the majority of people not working."

    McDaniel had railed against the federal "spending sprees" by Cochran, but his calls to slash the budget unnerved some voters.

    Frank McCain, a 71-year-old retired tax administrator from Mendenhall, voted for Cochran.

    "I believe he is doing a good job," McCain said. "But mostly I'm more scared of the other candidate. He wants to do things like not taking school funding when everyone else is."

    Kellie Phipps, a 42-year-old public school teacher from Taylorsville, voted for McDaniel. "I think we need some new blood," Phipps said.

    In November, Cochran will face Democrat Travis Childers, a former congressman, in the heavily Republican state.

    Fox News' John Roberts and The Associated Press contributed to this report.