The Board of Peace, as envisioned in a charter signed last month, has divided several U.S. allies, including France and a number of other European nations that declined to join at this time. Critics have called it the latest example of Mr. Trump’s efforts to dismantle the post-World War II international system, and analysts say he is trying to create a rival to the United Nations that puts him in charge. As chairman, he would have veto power over some of the body’s decisions.