"I have apologized one time. The apology was accepted by the president, by the vice president, who I know. I am not apologizing again," said the South Carolina Republican.
Wilson told Wallace he'd had a "town hall" moment.
Wilson noted that he had apologized to the president on Wednesday, adding, "That is sufficient." The apology was delivered over the telephone to White House Chief of Staff Rahm Emanuel, and was accepted publicly by Obama.
That means Wilson will likely be brought to the well of the House floor this upcoming week so House Speaker Nancy Pelosi can sanction him with a resolution of "disapproval."
"My view is that the apology to the president, to the White House, his acceptance, the vice president's acceptance -- people know my civility. They know that this was a one-time event, and it was out of frustration."