Rep. Joe Wilson said Sunday that he will not apologize on the House floor for his outburst during President Obama's health care address, even though Democratic leaders have threatened to formally discipline him if he does not. 

Wilson noted that he already apologized directly to the White House after shouting, "You lie," to the president during his Wednesday address to a joint session of Congress. The outburst triggered a political firestorm, but Wilson told "FOX News Sunday" that Democrats are just "playing politics" by trying to drag out the issue and force another apology. 

"I've apologized one time. The apology was accepted by the president, the vice president. ... I am not apologizing again," he told "FOX News Sunday." "I believe that is sufficient." 

Wilson said he would "never do something like that again," but continued to defend himself. 

The South Carolina Republican on Wednesday accused the president of lying for claiming his health care reform plan would not cover illegal immigrants. 

"I believe in the truth. What I heard was not true," Wilson explained Sunday. "I believe (Obama) was misstating the facts." 

Wilson said he felt "provoked" and attributed the outburst to a "town hall moment," referring to the town hall meetings where constituents frequently shouted out their frustrations over health care reform. 

While Democrats' health care plans do not provide for coverage of illegal immigrants, they also do not include verification mechanisms for determining legal status -- Republicans have long said this leaves open the door for illegal immigrants to obtain coverage on taxpayer dollars. 

But Wilson said he was proven right, since the Senate Finance Committee and the White House are now considering such verification mechanisms and other stricter measures.  

Aside from his apology to the White House, Wilson also issued a written statement apologizing for his outburst on Wednesday. 

But while House Speaker Nancy Pelosi indicated immediately afterward that Wilson had done enough, Democratic leadership has since decided to seek a public apology from Wilson to his colleagues on the House floor. 

If he does not, a resolution to punish him could come as early as Tuesday. 

Sen. Lindsey Graham, another Republican from South Carolina, said on "FOX News Sunday" that Wilson has made clear that "what he did was wrong." 

"He has apologized to the president. That's enough for me. It's good that the president accepted it. But I'd like to see this matter end," Graham said.