Updated

Rival presidential candidates Mitt Romney and Newt Gingrich are set to appear at the same breakfast restaurant at the same time on the day of the South Carolina primary.

Both campaigns said Friday they will not change schedules that, by coincidence, have the dueling candidates visiting Tommy's Country Ham House in Greenville at 10:45 a.m. EST.

Romney and Gingrich are locked in a nasty, neck-and-neck fight to win the first-in-the-South primary. They have criticized each other repeatedly on the debate stage, in TV ads, on the radio, in mail and in telephone calls.

Gingrich has surged ahead in recent days, eating into Romney's lead in polls and threatening what had appeared to be a swift march to the nomination.

Romney campaign spokesman Rick Gorka called the scheduling a "pure coincidence and we are not changing our schedule."

Gingrich campaign spokesman Nathan Naidu said Gingrich's schedule came out first and that Gingrich is "more than happy to treat Gov. Romney to ham at our event."