Cochran challenger building evidence towards legal action against Mississippi ...

(CNN) -- The tea party-backed challenger who narrowly lost a Republican primary runoff in Mississippi to longtime Sen. Thad Cochran is announcing a legal challenge contesting those results.

Noel Fritsch, spokesman for state Sen. Chris McDaniel, told CNN Chief Congressional Correspondent Dana Bash Monday that they've found thousands of examples of voter irregularities, as well as invalid crossover votes from Democrats. Fritsch said it's on that basis that McDaniel officially announced a legal challenge later Monday at a news conference at the Hinds County courthouse in Jackson, Mississippi.

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McDaniel's news conference comes just two hours before the deadline for the state GOP to hand over to the Mississippi secretary of state's office the certified results from the runoff contest.

McDaniel narrowly edged Cochran in a June 3 primary, but with neither man cracking the 50% threshold needed to win, the contest moved to the runoff three weeks later, which Cochran won by fewer than 7,000 votes.

His victory was apparently aided by votes from African-American Democrats, who were actively courted during the runoff by Cochran's campaign and allied groups. According to Mississippi law, voters are not required to register with a political party, and anyone who doesn't vote in a primary election can cast a ballot in either party's runoff.

After the runoff, McDaniel's campaign dispatched volunteers across Mississippi to investigate the results in the state's 82 counties. FreedomWorks, one of the anti-establishment groups that's been supporting McDaniel, dispatched activists to assist the campaign. Separately, a conservative outside group filed a lawsuit in federal court asking for full access to the voting records in the primary and runoff elections.

While Fritsch said there were thousands of voter irregularities, he could not provide an exact number. But he added that the irregularities they've they have found so far do not include any from absentee ballots - just votes that occurred in person in the runoff. After the runoff, McDaniel's campaign dispatched volunteers across Mississippi to investigate the results in the state's 82 counties.

McDaniel: 'Better we learn to stand and fight'

McDaniel said Friday on CNN's 'New Day' that 'the integrity of the process matters. We believe on that night of June 24 there were thousands of irregularities and we've already found thousands of irregularities in the process.'

'Right now, we have found we have found more than 5,000 irregularities. There are more than 19,000 absentee ballots we still haven't seen yet,' McDaniel added.

McDaniel also defended his campaign's offer - announced Thursday - of rewards of $1,000 each for individuals providing 'evidence leading to the arrest and conviction of anyone involved in voter fraud.'

The Cochran campaign has disputed McDaniel's claims, and numbers. The Cochran campaign said Monday afternoon that it has representatives at all 82 courthouses to monitor the review of the ballot boxes, and that its pleased so far with the results.

'The county-by-county results reported thus far are revealing an extremely low number of crossover votes from the June 24th election. As the process moves forward, the conversation is shifting from wild, baseless accusations to hard facts,' Cochran spokesman Jordan Russell told CNN. 'As we have said from the beginning, the run-off results are clear: the majority of Mississippians voted for Senator Thad Cochran.'

CNN Political Editor Paul Steinhauser and CNN's Jeremy Diamond contributed to this report