(CNN) -

A Mississippi judge has tossed out state Sen. Chris McDaniel's challenge to that state's June 24 GOP primary runoff results, ending another chapter in one of the most bitterly contested U.S. Senate primaries in recent memory and bringing longtime Sen. Thad Cochran one step closer to another term in Washington.

Special Judge Hollis McGehee ruled that McDaniel waited too long to file his challenge with state Republican Party. McDaniel filed the challenge 41 days after the election; McGehee said that under state law the challenge had to be filed within 20 days.

McDaniel's campaign did not immediately indicate whether it would appeal McGehee's ruling. CNN reached out to the McDaniel campaign, but did not receive a response.

McDaniel, who received strong support from tea party and anti-establishment groups, narrowly edged Cochran in Mississippi's June 3 Republican primary. But neither candidate cracked the 50% threshold needed to win, forcing a runoff three weeks later that Cochran won by slightly more than 7,000 votes.

Cochran's victory was apparently aided by crossover votes from African-Americans, a largely Democratic bloc actively courted by Cochran's campaign and allied groups.

In the statement announcing its challenge, McDaniel's campaign claimed there was evidence of election fraud, including insecure ballot boxes and fraudulent voting. Among other things, McDaniel's supporters argued that African-American Democrats improperly voted in the Republican runoff after participating in the Democratic primary.

Cochran's campaign pushed back against McDaniel's argument, attributing unusual levels of support from African-Americans to four decades of relationship-building in the state.

Under 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.