WARSAW — It was supposed to be a summit meeting of historical adversaries that gathered to unite against a common foe, Iran. But any expectation that nations with deep-rooted conflicts of their own would display a newfound amity seemed troubled from the start.

For a number of Trump administration officials, including Mike Pence, a vice president who has gained much of his foreign policy experience on the job, solving the problem seemed to be as simple as sharing a meal.

“I believe we are beginning a new era,” Mr. Pence said Wednesday night at a dinner in the Polish capital, Warsaw. It was part of a summit meeting organized by the Trump administration that drew together officials from Middle Eastern countries — including Israel, Saudi Arabia, Qatar and Yemen — that are known for being on opposing, not cooperating, sides.

The vice president said he looked forward to Prime Minister Benjamin Netanyahu of Israel and the foreign ministers of Bahrain, Saudi Arabia and the United Arab Emirates “all breaking bread together and, later in this conference, sharing honest perspectives on the challenges facing the region.”