The ad, with a big picture of a smiling Mr. Cochran, asked Democrats to vote for him. It cited the senator as having received praise from Democrats and Republicans alike for providing more than $18 million to Mississippi’s historically black colleges and universities.

“The decision on who is going to be our next senator is going to be made in the republican primary,” the text at the bottom of the ad reads, keeping the names of the political parties in lowercase. “We’re asking democrats to cross over and vote in the republican primary to ensure our community’s interest is heard.”

Mr. Cochran was unable to win a majority of votes in the Republican primary June 3. He faces Chris McDaniel, a state senator, in a June 24 runoff election.