Paul's resignation follows that of Intel CEO Brian Krzanich and Under Armour CEO Kevin Plank, who left the president's council over his response to the Charlottesville, Va., attack last weekend. "We should honour - not attack - those who have stood up for equality and other cherished American values".
Trump called Frazier one of the "great, great leaders of business in the country" at a July 30 event at the White House.
Kenneth Frazier, who is the CEO of Merck, has quit an advisory panel and criticised a racist protest in Virginia over the weekend, which left a woman dead.
But by the time he arrived at midmorning, it was clear all other messages would be drowned out until he said more about Charlottesville.
As it stands, Johnson & Johnson's Axel Gorsky is the remaining senior pharma figure on the Manufacturing Council, and as of this morning had not revealed whether or not he will remain on board.
Sessions also says he is meeting with President Donald Trump and officials from the Federal Bureau of Investigation on Monday to discuss the recent violence in Charlottesville, Virginia.
On Saturday, Trump said the hatred, bigotry and violence in Charlottesville need to end on "many sides".
The departure of Kenneth Frazier from the president's American Manufacturing Council added to a storm of criticism of Trump over his handling of Saturday's violence in Charlottesville, in which a woman was killed when a man drove his auto into a group of counter-protesters.
Mr Trump mocked the executive nearly immediately following the resignation, saying on Twitter that Mr Frazier will now "have more time to LOWER RIPOFF DRUG PRICES!"
Trump swiftly hit back at Frazier on Twitter, saying the CEO would now "have more time to LOWER RIPOFF DRUG PRICES!". "Dow will continue to work to strengthen the social and economic fabric of the communities where it operates - including supporting policies that help create employment opportunities in manufacturing and rebuild the American workforce".
Lowering drug prices was a major campaign promise for Trump, and throughout the early part of the year, Trump made threatening and vague statements about the prices of drugs being too high.
But Trump had been criticized for not explicitly condemning white supremacists after violent clashes with counter-protestors turned deadly in the Virginia college town Saturday.
One of the nation's most prominent African American executives, Frazier did not mention Trump by name.
The White House said Sunday that Trump's remarks condemning violence at a white nationalist rally were meant to include the Ku Klux Klan and neo-Nazi groups.
"The AFL-CIO has unequivocally denounced the actions of bigoted domestic terrorists in Charlottesville and called on the president to do the same", Trumka said in a statement.
Goldman Sachs CEO Lloyd Blankfein tweeted: "Lincoln: 'A house divided against itself can not stand.' Isolate those who try to separate us".
SpaceX founder Elon Musk and Disney CEO Robert Iger bowed out of their respective positions when Trump said he would pull the US out of the Paris climate agreement.
An earlier decision from the president to reject the Paris Accords and its global compact to address climate change prompted the departure of tech's favorite chief executive, Elon Musk.