Senator Raphael Warnock uses a new ad to pressure Herschel Walker to commit to a debate.

ATLANTA — A new advertisement from Raphael Warnock, Georgia’s incumbent Democratic senator, pushes the state’s Republican Senate nominee, Herschel Walker, to debate Mr. Warnock.

“Stop dodging. Commit to debates,” reads an onscreen message in the 30-second television spot, which began airing in Georgia’s top four media markets on Tuesday, juxtaposed against Mr. Walker’s recent comments about his openness to debating Mr. Warnock.

The ad is part of a weekslong saga between the two candidates: While Mr. Walker has repeatedly pledged to debate Mr. Warnock, his campaign has not accepted invitations to any of the three matchups scheduled for this fall. Mr. Warnock has committed to attending an Oct. 16 debate hosted by the Atlanta Press Club, in addition to two others in Macon and Savannah later that month; those dates have not yet been finalized.

During a news conference in Athens, Ga., last Wednesday, Mr. Walker told reporters that he would be “ready to go” for the Oct. 16 debate if the two campaigns “negotiate and we get everything right.”

His spokeswoman, Mallory Blount, later issued a statement saying that Mr. Walker’s campaign “doesn’t care about the old way of doing things” and that any debate it ultimately agreed to “must have a fair and equitable format and unbiased moderator.”

Mr. Warnock’s campaign has used Mr. Walker’s hesitance to underscore its argument that he is not prepared to serve in the Senate.

“I don’t know if Herschel Walker is scared for voters to hear what he has to say, or scared for voters to hear that he’s unprepared to speak on the issues that matter most to the people of Georgia,” Quentin Fulks, Mr. Warnock’s campaign manager, said in a statement. “There’s a clear choice in the race for Senate, and we hope Herschel Walker will be true to his word and commit to joining us at three debates.”