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.

Mrs. Clinton, in a speech shortly after the deal was struck, embraced its terms but also called for enforcement so strict that the United States would leap upon any violation.

One of the most interesting elements of Mr. Ryan’s 35-minute bagels-and-coffee breakfast with a group of reporters was his argument that Mr. Obama was right to be concerned about engaging America in new conflicts but had taken caution to a paralyzing extreme.

“He is in a massive retrenchment,” Mr. Ryan said. “I think he has gone way too far.”

Mr. Ryan said the Middle Eastern leaders he met were concerned about America’s long-term direction, especially that Washington is willing to let Iran take on a larger role in the Middle East. Those conversations appeared largely in line with what Secretary of State John Kerry confronted in his own encounter with Sunni Arab allies in Bahrain last week.