Former US presidents George HW Bush and George W Bush have said "America must always reject racial bigotry, anti-Semitism and hatred in all forms".
Their statement, following clashes between white supremacists and counter protesters in Charlottesville, does not mention Donald Trump.
The current President is under pressure over his reaction to the violence.
He condemned the far-right groups involved, but then insisted counter-protesters were also to blame.
It comes after he abruptly abolished two of his White House business councils in the latest fallout from his combative comments on racially charged violence in Charlottesville, Virginia.
The president announced the action via tweet, although only after one of the panels had already agreed to disband earlier in the day.
A growing number of business leaders on the councils had openly criticised his remarks laying blame for the violence at a white supremacists rally on "both sides".
Mr Trump tweeted: "Rather than putting pressure on the businesspeople of the Manufacturing Council & Strategy & Policy Forum, I am ending both. Thank you all!"
Rather than putting pressure on the businesspeople of the Manufacturing Council & Strategy & Policy Forum, I am ending both. Thank you all!— Donald J. Trump (@realDonaldTrump) August 16, 2017
The decision came as the White House tried to manage the repercussions from his defiant remarks a day earlier.
Some Republicans and scores of Democrats denounced Mr Trump's comments as putting white supremacists on equal moral footing with counter-protesters in Charlottesville and called for an apology.
Most of those Republicans, including congressional leaders, did not specifically criticise the president.
Mr Trump himself stayed out of sight, tweeting occasionally about a primary in Alabama, the stock market and, once, his campaign slogan. At noon he travelled from New York to his golf club in New Jersey for the night.
The president told associates he was pleased with how his press conference went, saying he believed he had effectively stood up to the media, but business leaders felt differently.
Denise Morrison, chief executive of Campbell Soup, declared she was leaving the manufacturing council, saying "the president should have been - and still needs to be - unambiguous" in denouncing white supremacists.
Chief executives had begun tendering their resignations from White House panels after Mr Trump's initial comments following the Saturday violence, when he said there were "very fine people, on both sides".
The first to step down, Kenneth Frazier of Merck, drew a vicious Twitter response from the president. Later, Mr Trump called those who were leaving "grandstanders" and insisted many others were eager to take their places.
But on Wednesday members of the Strategy and Policy group, led by Blackstone chief executive Stephen Schwarzman, concluded after a 45-minute conference call that they would end the council and announce their decision in a statement.
In a subsequent call with Mr Trump, the president agreed it was the right course of action. He tweeted before they could announce the decision they had reached - making it appear it was his choice.
Publicly criticising the president and resigning from his councils is a significant step for big-name corporate leaders.
Though the policy influence of such advisory groups is sometimes questionable, simply meeting Mr Trump in front of the TV cameras is valuable face-time for the executives - and for the president.
Though not as outspoken as the business leaders, some fellow Republican leaders are going after Mr Trump forcefully, too.
Senator Lindsey Graham of South Carolina said the president "took a step backward by again suggesting there is moral equivalency" between the marching white supremacists and the people who had been demonstrating against them.
Ex-presidential candidate Mitt Romney tweeted: "No, not the same. One side is racist, bigoted, Nazi. The other opposes racism and bigotry. Morally different universes."
No, not the same. One side is racist, bigoted, Nazi. The other opposes racism and bigotry. Morally different universes.— Mitt Romney (@MittRomney) August 16, 2017
Several White House aides told colleagues they were dismayed with Mr Trump's remarks about Charlottesville, but no-one moved to leave the administration.
Chief strategist Steve Bannon told associates he thought Mr Trump's performance would electrify his conservative base. Mr Bannon's job has been in question, with Mr Trump refusing to say he had confidence in him.
In an interview published on Wednesday by The American Prospect, a liberal magazine, Mr Bannon dismissed "ethno-nationalists," calling them "losers," ''a fringe element" and "a collection of clowns".
As Mr Trump navigates this latest controversy, the White House said his aide Hope Hicks would temporarily step into the role of communications director. She is White House director of strategic communications, and a near-constant presence at the president's side.
She served as spokeswoman for Mr Trump's presidential campaign and worked for years in public relations for the Trump Organisation and his daughter's fashion and lifestyle brand.