Frazier announced Monday he would resign from the council "as a matter of personal conscience" following the violence this weekend in Charlottesville, where one person died and many more were injured in clashes between white supremacists and counterprotesters.
A woman was killed on Saturday when a vehicle rammed into a crowd protesting against a white supremacist rally.
Trump's initial failure Saturday to denounce white supremacist groups by name - instead he bemoaned violence on "many sides" - prompted criticism from fellow Republicans as well as Democrats.
Frazier announced early in the day that he was leaving Trump's advisory council, saying, "I feel a responsibility to take a stand against intolerance and extremism".
In February, he stood next to the president in the White House to announce a $7 billion investment in a new USA factory.
Krzanich said Monday night that his resignation was an attempt to "call attention to the serious harm our divided political climate is causing to critical issues, including the serious need to address the decline of American manufacturing".
The president followed up later in the day, tweeting that Merck "is a leader in higher and higher drug prices while at the same time taking jobs out of the US". In an indirect, yet very pointed, criticism of President Trump, Krzanich wrote in a company blog post, "I resigned because I want to make progress, while many in Washington seem more concerned with attacking anyone who disagrees with them".
Krzanich also said he had urged other leaders to condemn the white supremacists who took part in the Virginia rally.
"First of all, the council was sort of a joke", Mr Trumka, president of the AFL-CIO, the largest group of unions in the United States, told CNN.
But at least seven companies or executives said that they would remain with the council, which was formed in January to advise Trump on manufacturing growth - a key focus of the president's campaign.
"I'm resigning from the Manufacturing Jobs Initiative because it's the right thing for me to do", Alliance for American Manufacturing President Scott Paul wrote on Twitter.
The parade of departing leaders from the informal panel now includes the chief executives for Merck, Under Armour and Intel and the president of the Alliance for American Manufacturing.
Trump has not said if who will join his council as replacements.
Trump told reporters in Bedminster, New Jersey, on Saturday that he condemned "in the strongest possible terms this egregious display of hatred, bigotry and violence on many sides".
Still, the statement was attributed to an unnamed spokesperson, not to Trump himself.
The resignation prompted an angry response from Trump on Twitter.
Drugmakers have come under withering criticism for soaring prices in the USA, including by Trump, though he has yet to act on a promise to contain them.