Story highlights Sen. Orrin Hatch, R-Utah, tweeted this weekend: 'We should call evil by its name'

President Donald Trump made a new statement on Monday

(CNN) Following the white supremacist rally in Charlottesville, many Republican lawmakers went farther than the President in condemning the violence and actions that took place and urged him to call out white supremacy by name.

Their comments came over the weekend, before Trump more directly rebuked the "KKK, neo-Nazis, white supremacists, and other hate groups," calling them "repugnant to everything we hold dear as Americans" in comments Monday at the White House.

Sen. Tim Scott, the only black Republican in the Senate, said that while he appreciated Trump's statement Monday, it would have made more of an impact if he'd said it on Saturday.

"Today, the President's remarks were clear and specific. However, they would have been more impactful on Sunday," Scott tweeted. "I hope this serves as a lesson for all that when a community grieves, when Americans look for guidance after such a crushing and devastating attack like the one that unraveled this weekend in Charlottesville, we must take a firm stance against hate and violence."

Other Republicans praised Trump's second statement Monday. Sen. James Lankford, a Republican from Oklahoma, applauded the President in a statement Monday afternoon for "clearly communicating the evilness of racism" and for calling out the white supremacist groups.