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.
Lankford earlier this weekend condemned "the supremacy of any race over another," in a tweet that didn't mention Trump by name.
Sen. Lindsey Graham, a South Carolina Republican and frequent critic to the President, tweeted following
Trump's remarks, "Well done Mr. President."
Sen. Orrin Hatch, the longest-serving Republican in the Senate, invoked the memory of his own brother
in a powerful tweet signed with his initials and saying "we should call evil by its name."
"We should call evil by its name. My brother didn't give his life fighting Hitler for Nazi ideas to go unchallenged here at home. -OGH" he tweeted.
Sen. Marco Rubio, R-Florida, tweeted Saturday evening
it was "very important" for Trump to name the incidents that took place for "what they are, a terror attack by #whitesupremacists."
Rubio joined others who criticized Trump for not singling out white supremacists in his statement Saturday when he condemned what he called the "egregious display of hatred, bigotry and violence." This came after a man allegedly plowed into a group of counter-protesters, killing one woman.
Much of the criticism centered around Trump blaming "many sides" for the violence.
"On many sides. It's been going on for a long time in our country. Not Donald Trump, not Barack Obama, it's been going on for a long, long time. It has no place in America," he said Saturday.
Republican Rep. Ileana Ros-Lehtinen of Florida, however, tweeted
"there are no other 'sides' to hatred and bigotry."
Sen. Cory Gardner said Sunday on CNN's "State of the Union" that the President should be more specific in going after white nationalists.
"This is not a time for vagaries," the Republican from Colorado told CNN's Jake Tapper
. "This isn't a time for innuendo or to allow room to be read between the lines. This is a time to lay blame -- to lay blame on bigotry, to lay blame on white supremacists, on white nationalism and on hatred. And that needs to be said."
Rep. Carlos Curbelo, R-Florida, pointed out
that the President has "always called out radical Islamic terrorists" by name and called on him to do the same with white supremacy.
Meanwhile, Sen. Ted Cruz called on the Department of Justice
to "immediately investigate and prosecute this grotesque act of domestic terrorism."
And Sen. Dean Heller, R-Nevada, blasted a Nevada student who was spotted at the rally.
"I don't know this person & condemn the outrageous racism, hatred and violence. It's unacceptable & shameful. No room for it in this country."