Story highlights The South Carolina Republican senator said 'Trump took a step backward'

Lindsey Graham added his voice to Republicans distancing themselves from Trump

Washington (CNN) The feud between President Donald Trump and Sen. Lindsey Graham over the President's response to racially motivated protests in Charlottesville, Virginia, continued Thursday, with the South Carolina senator accusing Trump of stoking tensions, a claim Trump called "a disgusting lie."

"Your tweet honoring Miss Heyer was very nice and appropriate. Well done," the South Carolina lawmaker said Thursday morning, referring to Heather Heyer, the 32-year-old woman who was killed in a car attack on Saturday. The man charged in her killing has been described as a Nazi sympathizer.

"However, because of the manner in which you have handled the Charlottesville tragedy, you are now receiving praise from some of the most racist and hate-filled individuals and groups in our country. For the sake of our nation -- as our President -- please fix this."

"History is watching us all," added Graham, who has been one of the few Republican lawmakers to directly denounce Trump's equivocation earlier this week between white supremacists and those who were protesting them in Charlottesville. The President blamed "both sides" for inciting violence and said there were "very fine people" protesting in the Virginia city amid the torch-bearing protesters.

Shortly before Graham's statement Thursday, the President accused the South Carolina Republican of lying about his response to Charlottesville.

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