WASHINGTON — Treasury Secretary Steven Mnuchin, whose fellow Yale alumni called for him to resign because they thought he was slow to denounce hate groups after violence in Charlottesville, Va., last month, came under fire Friday from another rarefied academic realm: the former students of his private country day school.

In a letter to Mr. Mnuchin, 185 graduates of Riverdale Country School in New York — considered one of the best and most exclusive private schools in the country — said that they were “deeply troubled” by President Trump’s response to violence incited by neo-Nazi and white supremacist protests in August. They said that Mr. Mnuchin showed a lack of moral leadership when he defended Mr. Trump, who condemned both the racist protesters and the counter-protesters who clashed in Virginia.

“Like your classmates from Yale, we believe your resignation would be the most honorable choice,” they wrote.

It was only the latest hit on the beleaguered Treasury secretary as he tries to shepherd a challenging rewrite of the tax code through Congress in the coming months. The Treasury Department’s inspector general is looking into Mr. Mnuchin’s inquiry into whether he could use a military plane for his European honeymoon last month. His new bride, Scottish-born actress Louise Linton, took heat — then apologized — for her dismissive response to critics who objected to the lavish lifestyle that she chronicled on social media as she traveled on the taxpayer’s dime.