Mr. Romney, a former Massachusetts governor, was the last to arrive at the Fox News offices in Midtown Manhattan. He came in with his wife, Ann, and a smattering of aides and travel staff, and they quickly settled into a small conference room near the 12th-floor studio.

Spotting the reporter, Mr. Romney’s aides sprang into action, questioning where he worked and what he was doing there, and then insisting that he not physically approach Mr. Romney before or after he was questioned on television by the attorneys general and Mr. Huckabee.

The request was reiterated to executives at Fox News.