State Sen. Chris McDaniel lost the GOP runoff election to U.S. Sen. Thad Cochran in June. (AP Photo/the Clarion-Ledger, Greg Jenson)

Mississippi state Sen. Chris McDaniel (R) said Friday that he will announce a "major development" on Monday related to the results of the June 24 GOP runoff election he lost to U.S. Sen. Thad Cochran.

McDaniel said in a news release that he will hold a press conference at his attorney's office Monday afternoon. He did not specify what he will say. But it may be an announcement that he is officially challenging the results of the election, as his legal team has said it expects to do.

Cochran was certified by the Republican Party of Mississippi in July as the winner of the runoff by 7,667 votes. But McDaniel has refused to concede. His campaign has raised the possibility of voter fraud. But so far, it has not come forward with specific evidence.

McDaniel attorney Mitch Tyner told reporters on July 16 that "there is already evidence to file a challenge." He said that "crossover votes" would likely be a big part of the challenge, but did not make specific allegations.

The crossover reference was apparently to Democrats who voted in both the Democratic primary and Republican runoff.