Darwin-born Mr Liveris, chairman and chief executive of the Michigan-headquartered Dow Chemical Company, announced on Tuesday he would not join the growing list of business leaders quitting US President Donald Trump's American Manufacturing Council.
"America's leaders must honor our fundamental values by clearly rejecting expressions of hatred, bigotry and group supremacy, which run counter to the American ideal that all people are created equal", said Frazier, who is black.
The White House and Trump have come under fire after Trump faulted "many sides" for the violence while failing to mention the far-right militia groups involved in the Charlottesville riot - some of whom were allegedly wearing Trump hats and T-shirts.
"Hate and intolerance are a betrayal of what we stand for as Americans", said Pepsi chief executive Indra Nooyi, in a statement that did not address the Trump panel.
Frazier announced his decision as criticism was mounting of Trump's failure over the weekend to explicitly denounce the neo-Nazis and Ku Klux Klan members whose rally in Charlottesville, Virginia set off violent clashes.
Privately, many chief executives say they are fuming, outraged by the president.
Individually, at least one CEO, John Maraganore of Alnylam Pharmaceuticals, tweeted his support, saying he was "proud to stand with leaders like Ken Frazier". "Promoting American manufacturing should not be a political issue", Krzanich wrote in a tone sure to echo many others in Silicon Valley.
The White House tried to stem the damage on Sunday.
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President Trump's manufacturing council keeps on shrinking.
Many corporate leaders have faced a lose-lose scenario in which any choice involving politics can alienate customers, not to mention a USA president who has shown a willingness to personally negotiate government contracts.
What will the absence of these CEOs mean for the president's business council?
Richard Trumka, President of the 12.5-million-member AFL-CIO, announced on Tuesday: "I can not sit on a council for a President that tolerates bigotry and domestic terrorism".
SpaceX founder Elon Musk and Disney CEO Robert Iger bowed out of their respective positions when Trump said he would pull the USA out of the Paris climate agreement. But they also said they'd stay on the council so they could advise the government on ways to strengthen manufacturing.
Former Uber Technologies Inc [UBER.UL] CEO Travis Kalanick quit the business advisory council in February amid pressure from activists and employees who opposed the administration's immigration policies.
On Sunday, however, the White House added: "The president said very strongly in his statement yesterday that he condemns all forms of violence, bigotry, and hatred, and of course that includes white supremacists, KKK, neo-Nazi, and all extremist groups".
Marc Benioff of Salesforce aimed at Trump with a sarcastic post, saying: "Thank you @realDonaldTrump for calling to Love thy neighbor, value equality, & calling evil by name".
"I have already made clear my abhorrence at the recent hate-spawned violence in Charlottesville, and earlier today I called on all leaders to condemn the white supremacists and their ilk who marched and committed violence", Krzanich said. "He called for national unity and bringing all Americans together".