In an interview on MSNBC, Burns initially defended the tweet, saying his decision to post the cartoon was born out of a frustration with African Americans voting against their own interests and politicians who "tap dance" for votes but disappear after taking office.
"I see African Americans in many cases – not every case – but in many cases are suffering throughout this country," he said. "En masse, we have been voting for the Democratic party – en masse – and yet, I think we have very little to show for it."
He referenced a photo purported to show Clinton standing beside her husband while in blackface years ago, although the photo has been widely debunked.
He apologized in an 11 minute-long video posted Monday night on Periscope.
"It was not at all my intention to offer or to not offend anyone," Burns said. "I really am a shepherd to God's people, and the last thing I want to do is offend people."
He said he was instead aiming to shine a spotlight on pandering done by Democratic politicians.
"The last thing I want to do is to anger people," he said. "I really am a unifier. I know God has called me to bring people together so that they can see the good out of each and every one of us, and you can see the good out of every neighbor."