Lindsey Graham; Donald Trump (copy)

U.S. Sen. Lindsey Graham, R-S.C. (left), and President Donald Trump. File/Rainier Ehrhardt, John Locher/AP

President Donald Trump blasted U.S. Sen. Lindsey Graham on Twitter Thursday morning, calling the South Carolina senator a "publicity seeking" lawmaker after Graham criticized Trump for his response to the Charlottesville, Va., demonstrations and violence.

In a series of tweets starting at 6:19 a.m., Trump said Graham falsely accused him of offering "moral equivalency" between white supremacist groups and counter protesters, like Heather Heyer, who were protesting the hate groups last weekend.

Heyer, 32, was killed Saturday when she was struck by a car driven into the crowd by an Ohio man alleged to have far-right views. He faces multiple criminal charges, including second-degree murder.

"Such a disgusting lie," Trump tweeted of Graham's comments. "He just can't forget his election trouncing.The people of South Carolina will remember!"

Two hours and 41 minutes later, Graham hit back.

"Mr. President,” Graham began, "like most I seek to move our nation, my state, and our party forward - toward the light - not back to the darkness."

"Your tweet honoring Miss Heyer was very nice and appropriate. Well done," Graham continued. "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."

In his final tweet to the president, Graham warned Trump: "History is watching us all."

The Twitter spat Thursday came one day after Graham said that Trump's rhetoric is "dividing Americans."

In that same statement Wednesday, the South Carolina Republican said others in the GOP do not agree with the comments Trump made Tuesday, in which the president doubled down on his earlier statements that there is "blame on both sides" for the deadly rally in Charlottesville.

Graham said Republicans "will fight back against the idea that the Party of Lincoln has a welcome mat out for the David Dukes of the world."

Earlier this week, Graham also called on Attorney General Jeff Sessions to go to Virginia and "personally handle domestic terrorism investigations" and alleged civil rights abuses by the Ku Klux Klan and neo-Nazis.

Graham additionally proposed the Departments of Justice and Homeland Security form a task force on the threat of white supremacist groups and report back to Congress with potential solutions for cracking down on them.

"This is an opportunity for the Trump administration to come down like a hammer on white supremacists," Graham said during a news conference in his Columbia office. "And I hope they do."

Graham was not the only South Carolina lawmaker to criticize Trump for his response to the violent white supremacist rally in Charlottesville. In an interview Wednesday with The Post and Courier, U.S. Sen. Tim Scott said, "There is no doubt the last couple of days complicates this administration's moral authority."

The Associated Press contributed to this report.

Reach Caitlin Byrd at 843-937-5590 and follow her on Twitter @MaryCaitlinByrd.

Caitlin Byrd is a political reporter at The Post and Courier and author of the Palmetto Politics newsletter. Before moving to Charleston in 2016, her byline appeared in the Asheville Citizen-Times. To date, Byrd has won 17 awards for her work.