WASHINGTON — Secretary of State Mike Pompeo said on Tuesday that Iran appeared willing to negotiate over its missile program “for the first time,” in what he and President Trump presented as evidence that sanctions and military pressure were working, less than a month after the president halted a planned military strike against Iran.

But within hours of the statement to reporters, delivered before a cabinet meeting at the White House, the idea was shot down by Iran’s foreign minister, Mohammad Javad Zarif, who was in New York for a meeting at the United Nations. His spokesman said that the two men had misinterpreted Mr. Zarif’s public statements, in which he repeated past demands that if the United States “wants to talk about missiles, it should stop selling weapons, including missiles, to regional states.”

It was a clear reference to American weapons sales to Saudi Arabia, the United Arab Emirates and Iran’s other Arab adversaries.

The odd exchange, and the apparent misconstruing of Mr. Zarif’s comments, seemed to underscore the eagerness of the White House to turn weeks of confrontation with Iran into some kind of negotiating opportunity — and a reminder of how hard that will be to accomplish. Iranian officials have repeatedly said they would engage with Mr. Trump only after he rejoined the 2015 nuclear accord, which he withdrew from last year.