President Donald Trump took a swing at his favorite punching bag Thursday, claiming his comments about the deadly violence in Charlottesville were misrepresented by media.

"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 wrote on Twitter.

One protester was killed in violent clashes between neo-Nazi and so-called "Alt-Right" demonstrators and counter-protesters in the Virginia college town of Charlottesville  Saturday.

Both Democrat and Republican politicians criticized Trump's initial response -- when he condemned violence "on all sides" -- as inadequate.

On Monday he singled out the Klu Klux and neo-Nazis as "repugnant," but on Tuesday he returned to his original position and said there had been "blame on both sides."

Trump's weak condemnation of the racist far-right set off a political firestorm across the US political spectrum. World leaders also criticized Trump's response.

The US president also took aim at two fellow Republican senators, Lindsey Graham of South Carolina and Jeff Flake of Arizona.

"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 said. "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.

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.

Trump also blasted Flake, one of the few Republicans openly critical of the president.

"Great to see that Dr. Kelli Ward is running against Flake Jeff Flake, who is WEAK on borders, crime and a non-factor in Senate. He's toxic!" Trump tweeted.

Flake, who is running for re-election, wrote Tuesday: "We can't accept excuses for white supremacy & acts of domestic terrorism. We must condemn. Period."

He followed that up Wednesday by tweeting "We can't claim to be the party of Lincoln if we equivocate in condemning white supremacy."

Abraham Lincoln, the US president who freed the slaves and defeated the southern confederacy in the 1861-1865 civil war, is a prominent Republican and one of the most revered figures in US history.