It was a break in tradition for the Red Cross, which has held the ball at Mar-a-Lago every year since 2005, with the exception of 2013 and 2014.

“The Red Cross provides assistance without discrimination to all people in need, regardless of nationality, race, religious beliefs, sexual orientation or political opinions, and we must be clear and unequivocal in our defense of that principle,” the statement said.

On Friday, Nancy G. Brinker, founder of the Susan G. Komen organization, wrote a post on Facebook in support of the board’s decision to seek another venue for the yearly fund-raiser: “There are no excuses, parsing or moral relativism when it comes to racism, bigotry and violence. There are no ‘sides.’ They are always wrong. Period.”

During his remarks on Tuesday at the Trump Tower in Manhattan, the president insisted that it was unfair to label all of the white nationalist protesters as neo-Nazis or white supremacists. The “alt-left” counterprotesters “came charging with clubs in their hands,” he said, and “there is blame on both sides.”

“You had a group on one side that was bad. You had a group on the other side that was also very violent,” President Trump said. “Nobody wants to say that. I’ll say it right now.”

His words set off an avalanche of criticism that led to the resignation of all 16 members of the President’s Committee on the Arts and the Humanities and the collapse of two of the president’s advisory groups: the Manufacturing Jobs Initiative and the Strategic and Policy Forum.