In an email sent to supporters Friday night, McDaniel emphasized he won the "Republican" primary — an apparent reference to Cochran openly soliciting many Democrats to vote in the runoff.

"Thank you for all your help. You've done some amazing things.  On June 3rd we won the popular vote. On June 24th we won the Republican primary election. As you might have heard, we're not quite done," McDaniel wrote.

McDaniel then asked his supporters to reach out to a law firm, which he said was in need of volunteers.

"We are in the process of trying to ensure a fair and accurate election took place on Tuesday. And we need your help," he continued. "Our team will ... direct you on what you can do to help us in this battle to ensure the integrity of our election process here in Mississippi."