James Murdoch, the chief executive of 21st Century Fox Inc. and a member of the board of The Wall Street Journal parent News Corp, became the latest major U.S. business leader to criticize President Donald Trump’s response to white supremacist violence in Virginia over the weekend, calling it concerning to all Americans.

“What we watched this last week in Charlottesville and the reaction to it by the President of the United States concern all of us as Americans and free people,” Mr. Murdoch wrote in a “personal note” sent...