Then, in a lunchtime speech, Vice President Mike Pence shattered the fragile unity.

Addressing the officials as they met this month in Warsaw, Mr. Pence denounced the United States’ closest allies — Britain, France and Germany — for coddling “Iran’s murderous revolutionary regime.” He demanded they stop undermining American-led sanctions and follow President Trump in renouncing a nuclear deal the Europeans were trying to save.

Privately, Mr. Pompeo briefly erupted. Aides said he complained Mr. Pence had undermined diplomacy — which one European official said included near-agreement about imposing new sanctions on Iran’s ballistic missile tests — and prompted fresh headlines about trans-Atlantic tensions.

But publicly, Mr. Pompeo never voiced his anger, keeping relations with the White House stable.