But would he support a Democrat over Duke if that's what it took to keep the former Ku Klux Klan leader from winning?
Trump said he wanted to make clear that he rebukes Duke "as quick as you can say it."
"Because last time with another person in this position, I did it very quickly. And they said, 'He didn't do it fast enough,' " Trump said. "Rebuked. Is that OK? Rebuked, done."
"Just so you understand, I don't know anything about David Duke, OK?" Trump had said.
Trump was pressed three times by Tapper on whether he would distance himself from support from the Ku Klux Klan.
"I don't know anything about what you're even talking about with white supremacy or white supremacists," Trump said then. "So I don't know. I don't know -- did he endorse me, or what's going on? Because I know nothing about David Duke; I know nothing about white supremacists."
He later blamed his answer on a "bad earpiece."
Later on Sunday Trump's running mate, Indiana Gov. Mike Pence, also denounced Duke, over Twitter.
"Well said @realDonaldTrump on #MTP. There will never be a place in our party for that man or his hateful rhetoric."