The departing Democrat president suggested the Republican accepted the support of a KKK sympathiser and dithered when questioned over it.
Official Klan newspaper The Crusader had announced its support for Mr Trump in a front page editorial and former KKK grand wizard David Duke has recently backed the 70-year-old.
“If you disrespect women before you were president, you will disrespect women when you’re in office,” said Mr Obama, speaking at a North Carolina rally on Wednesday.
“If you accept the support of a Klan sympathiser, the Klan, and hesitate when asked about that support, then you’ll tolerate that support when you’re in office.”
Mr Trump has been quizzed relentlessly throughout the presidential election run-up over opinions of Mr Duke.
The former Apprentice USA frontman was seen embracing Mr Duke in February and Mr Trump was soon asked by CNN’s Jake Tapper whether he “unequivocally condemns” him.
“Just so you understand, I don’t know anything about David Duke, OK?” said the property mogul.
“I don’t know anything about what you’re even talking about with white supremacy or white supremacists.
“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.”
The quarterly Crusader newspaper wrote: “What made America great in the first place?
“The short answer to that is simple. America was great not because of what our forefathers did – but because of who our forefathers were.
“America was founded as a White Christian Republic. And as a White Christian Republic it became great.”
Speaking to the Washington Post, article author, Pastor Thomas Robb said: “It’s not an endorsement because, like anybody, there’s things you disagree with.
“But he kind of reflects what’s happening throughout the world. There seems to be a surge of nationalism worldwide as nationals reclaim their borders.”
Mr Trump’s campaign however, responding in a statement on Tuesday to the article, said: “Mr Trump and the campaign denounces hate in any form.
“This publication is repulsive and their views do not represent the tens of millions of Americans who are uniting behind out campaign.”
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