Update:  Sen. Lindsey Graham has responded to President Donald Trump's tweets Thursday morning.

Graham, also using Twitter as a forum, has challenged the president, saying, "Mr. President, like most I seek to move our nation, my state and our party forward - toward the light - not back to the darkness."

Original story: President Donald Trump took to Twitter early Thursday to respond to the backlash over his comments on the deadly violence in Charlottesville, Virginia, slamming Sen. Lindsey Graham and the media.

"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," he wrote, referring to Heather Heyer, the 32-year-old woman killed Saturday while protesting the white supremacist Unite the Right rally. "Such a disgusting lie. He just can't forget his election trouncing. The people of South Carolina will remember!"

Trump added: "The public is learning (even more so) how dishonest the Fake News is. They totally misrepresent what I say about hate, bigotry etc. Shame!"

On Wednesday, Graham, R-S.C., issued the following statement:

"Mr. President, I encourage you to try to bring us together as a nation after this horrific event in Charlottesville. Your words are dividing Americans, not healing them," Graham said, according to CNN. "Through his statements yesterday, President Trump took a step backward by again suggesting there is moral equivalency between the white supremacist neo-Nazis and KKK members who attended the Charlottesville rally and people like Ms. Heyer."

In a news conference Tuesday, Trump blamed "both sides" for the violence.

“You had many people in that group other than neo-Nazis and white nationalists," he said. "The press has treated them absolutely unfairly.”

He added: "You also had some very fine people on both sides."