"Publicity seeking Lindsey Graham falsely stated that I said there is moral equivalency between the KKK, neo-Nazis & white supremacists...And people like Ms. Heyer," Trump said on Twitter.
Heather Heyer, 32, was killed in Charlottesville on Saturday when a suspected white nationalist drove his car into a crowd protesting the far-right march.
"Such a disgusting lie," Trump continued. "He just can't forget his election trouncing. The people of South Carolina will remember!"
Trump appeared to be referring to his defeat of Graham in last year's presidential primary.
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"The public is learning (even more so) how dishonest the Fake News is. They totally misrepresent what I say about hate, bigotry etc. Shame!," the US president added.
Graham had said the US president "took a step backward" Tuesday "by again suggesting there is moral equivalency between the white supremacist neo-Nazis and KKK members who attended the Charlottesville rally" and people like Heyer.
Clashes broke out between far-right demonstrators and counter-protesters in the Virginia college town of Charlottesville Saturday.
Both Democrat and Republican politicians criticised Trump's initial response -- when he condemned violence "on all sides" -- as inadequate.
After a press conference on Monday in which he singled out the Klu Klux and neo-Nazis as "repugant", he appeared to move back to his previous position the following day.
He once again said there had been "blame on both sides", setting off a political firestorm.
As the crisis unfolded, senior business executives began dropping out of the White House economic advisory councils to the point that Trump on Wednesday announced he was scrapping them.
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