“Who else is going to lead the world to make the global commons more peaceful?” he asked, echoing a question Mrs. Clinton has posed when, borrowing from former Secretary of State Madeleine K. Albright, she has referred to the United States as the “indispensable nation.”

He talked mostly about how he would deal with the complicated Middle East, including how leaders there had critiqued the Iran nuclear accord recently when he took a trip through Israel and several Sunni Arab states with a congressional delegation. His website displayed a video of the trip that included his motorcades, his meetings and visits to the Western Wall and the Temple Mount.

But Mr. Ryan did not say he would walk away from the terms of the Iran nuclear deal or offer views, as Mr. Trump did in a recent interview with The New York Times, on how he would have negotiated a stronger one. Instead, he said America must strictly enforce its terms and impose new costs on Iran for its ballistic missile tests — which do not violate the deal but may violate a new United Nations resolution that calls upon Iran to refrain from testing any missile that can carry a nuclear weapon.