But some Republicans spoke out against Trump, using his name directly to emphasize that they don't agree with what he said in Trump Tower.
During his news conference, Trump blamed "both sides" in the protests and equated the white supremacists on one side with the counter-protesters on the other side.
Some Republicans, to avoid more conflict, denounced racism after Trump's news conference -- and some indirectly referred to his statements when they called him out.
Sen. Lindsey Graham, a strong critic of Trump, took a hard stance on Wednesday against Trump's remarks at the news conference.
"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," Graham said in a statement.
He continued: "Many Republicans do not agree with and will fight back against the idea that the Party of Lincoln has a welcome mat out for the David Dukes of the world."
Sen. John McCain, whom Trump called out at the news conference for not voting for the GOP health care bill
, tweeted, "There's no moral equivalency between racists & Americans standing up to defy hate& bigotry. The President of the United States should say so"
Sen. Marco Rubio, who ran against Trump in the GOP primary, tweeted in a thread, "Mr. President,you can't allow #WhiteSupremacists to share only part of blame. They support idea which cost nation & world so much pain"
Sen. Jeff Flake, a strong critic of Trump, tweeted, "We can't accept excuses for white supremacy & acts of domestic terrorism. We must condemn. Period."
Sen. Cory Gardner also used Trump's name to say he was wrong at a town hall in Colorado.
"The President was wrong," Gardner said when asked about Trump's comments blaming the left, according to Fox31 Denver, a CNN affiliate.
Sen. Jerry Moran also called out Trump by name, writing in a tweet: "White supremacy, bigotry & racism have absolutely no place in our society & no one - especially POTUS - should ever tolerate it"
Ohio Gov. John Kasich didn't tweet but instead told NBC's "Today Show"
on Wednesday that Trump's remarks were "pathetic."
"This is terrible. The President of the United States needs to condemn these kinds of hate groups," said Kasich, who ran against Trump in the Republican presidential primary. "The President has to totally condemn this. It's not about winning an argument."
Rep. Ed Royce tweeted, "The President needs to clearly and categorically reject white supremacists. No excuses. No ambiguity."
And Rep. Leonard Lance tweeted, "Mr. President, there is only one side: AGAINST white supremacists, neo-Nazis, anti-Semites & the KKK. They have no place in America or GOP."
Former Florida Gov. Jeb Bush, who also ran against Trump in the GOP primary, tweeted in a thread denouncing racism: "I urge @POTUS to unite the country, not parse the assignment of blame for the events in Charlottesville."
And Rep. Will Hurd told CNN's Wolf Blitzer on "The Situation Room" that Trump should "apologize ... Racism, bigotry, anti-Semitism of any form is unacceptable."
Republicans who didn't use Trump's name but denounced racism
Senate Majority Leader Mitch McConnell didn't respond directly to Trump after his news conference but instead released a statement after news that white supremacists are planning a rally in McConnell's home state of Kentucky.
"We can have no tolerance for an ideology of racial hatred," McConnell said in a statement, without using Trump's name. "There are no good neo-Nazis, and those who espouse their views are not supporters of American ideals and freedoms. We all have a responsibility to stand against hate and violence, wherever it raises its evil head."
House Speaker Paul Ryan also didn't use Trump's name directly but called the President out in opposition to what he said in the news conference.
Ryan tweeted, "We must be clear. White supremacy is repulsive. This bigotry is counter to all this country stands for. There can be no moral ambiguity."
Mitt Romney, the 2012 Republican presidential nominee who has been a strong critic of Trump since the 2016 election, also didn't use his name to call him out: "No, not the same. One side is racist, bigoted, Nazi. The other opposes racism and bigotry. Morally different universes."
GOP Rep. Ileana Ros-Lehtinen tweeted, "Blaming 'both sides' for #Charlottesville?! No. Back to relativism when dealing with KKK, Nazi sympathizers, white supremacists? Just no."
Former Presidents George H.W. Bush and George W. Bush released a joint statement where they denounced racism but didn't use Trump's name.
"America must always reject racial bigotry, anti-Semitism, and hatred in all forms," they said in a statement. "As we pray for Charlottesville, we are reminded of the fundamental truths recorded by that city's most prominent citizen in the Declaration of Independence: we are all created equal and endowed by our Creator with unalienable rights. We know these truths to be everlasting because we have seen the decency and greatness of our country."