WASHINGTON — A new merging of strategic interests between Saudi Arabia and Israel was on display on Thursday as two former officials from those countries appeared on the same stage to discuss their concerns about Iran’s actions across the Middle East.

In an appearance at the Washington office of the Council on Foreign Relations, a retired major general in the Saudi armed forces, Anwar Eshki, and a former Israeli ambassador close to Prime Minister Benjamin Netanyahu, Dore Gold, described their common interests in opposing Iran. It was the culmination of five meetings between the two men, who both run think tanks, though Mr. Gold will become the director general of Israel’s Ministry of Foreign Affairs on Sunday.

“We’re both allies of the United States,” Mr. Gold said after the presentation. “I hope this is the beginning of more discussion about our common strategic problems.”

Left unsaid was the fact that Saudi Arabia and Israel have never had diplomatic relations, or that the Saudi government has never formally acknowledged the existence of the Jewish state. But the two nations have quietly exchanged intelligence for years, particularly about Iran.