Trump and Flake have had a rocky relationship. Flake refused to vote for Trump in the presidential election, and earlier this year, Flake’s book, “Conscience of a Conservative,” was published, which can be seen as a strong rebuke of Trump.
Ward faced off against McCain for his Senate seat in 2016 and this year made controversial remarks about him after he revealed that he had a brain tumor.
Trump is reportedly expected to endorse one of Flake's challengers at a rally in Phoenix next Tuesday.
On Wednesday, referring to Trump’s remarks on Charlottesville, Graham said in a statement, “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. I, along with many others, do not endorse this moral equivalency.”
Trump wrote in a series of Twitter posts the next day, “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.”
“Such a disgusting lie,” Trump continued. “[Graham] just can’t forget his election trouncing.”
After those tweets, Graham released a statement 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 ... 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.”
After Trump addressed the country on Sunday — his second statement on Charlottesville — condemning the KKK, neo-Nazis and white supremacist groups by name and stating that “racism is evil,” Graham responded with a simple tweet: “Well done Mr. President.”
ABC News’ John Verhovek and Saisha Talwar contributed to this report.