The Apple boss said he did not agree there was a “moral equivalence” between white supremacists and “those who oppose them”.
President Trump has disbanded two business councils after top bosses resigned.
Tim Cook said Apple will also make donations to human rights charities.
In an email to staff obtained by BuzzFeed News, Tim Cook said: “I disagree with the president and others who believe that there is a moral equivalence between white supremacists and Nazis, and those who oppose them by standing up for human rights.
“Equating the two runs counter to our ideals as Americans.”
Tim Cook added that “in the wake of the tragic and repulsive events in Charlottesville, we are stepping up to help organizations who work to rid our country of hate”.
Apple will donate $1 million to both the Southern Poverty Law Center and the Anti-Defamation League. It will also match two-for-one any staff donations to these and several other human rights groups until September 30, the Apple boss said.
On August 16, Presidnet Trump said he was scrapping two business councils after more bosses quit over his handling of the violent clashes in Virginia.
Business leaders left the White House manufacturing council after the backlash against how he reacted to the far-right rally last weekend.
The clashes culminated in Heather Heyer’s death and 19 wounded when a car ploughed into a crowd of anti-fascist protesters.
President Trump’s reaction has sparked outrage and generated global headlines.
His announcement on Twitter came as the heads of 3M, Campbell Soup, Johnson & Johnson and United Technologies announced their resignations on August 16.
President Trump said: “Rather than putting pressure on the businesspeople of the Manufacturing Council & Strategy & Policy Forum, I am ending both.”
Before Donald Trump’s announcement, the Strategy and Policy Forum announced it was a joint decision to disband the council.
Businesses have been under pressure to distance themselves from President Trump over his handling of the clashes in Charlottesville, Virginia.
On August 14, President Trump belatedly condemned the white supremacist and neo-Nazi groups that rallied in a small Virginia town on August 13.
However, in a rancorous news conference on August 15, the president backtracked and again blamed left-wing counter-protesters for the violence too.
On August 16, JPMorgan CEO Jamie Dimon, a member of the Strategy and Policy Forum, released a separate statement saying he strongly disagreed with President Trump’s recent statements, adding that “fanning divisiveness is not the answer”.
“Constructive economic and regulatory policies are not enough and will not matter if we do not address the divisions in our country. It is a leader’s role, in business or government, to bring people together, not tear them apart,” he said.
Denise Morrison of Campbell Soup said she could not continue to participate in the advisory panel after President Trump’s comments. Activists had called on Campbell Soup, among other firms, to take action.
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