PITTSBURGH  On Tuesday evening in New York, top officials of the world nuclear watchdog agency approached two of President Obama’s senior advisers to deliver the news: Iran had just sent a cryptic letter describing a small “pilot” nuclear facility that the country had never before declared.

The Americans were surprised by the letter, but they were angry about what it did not say. American intelligence had come across the hidden tunnel complex years earlier, and the advisers believed the situation was far more ominous than the Iranians were letting on.

That night, huddled in a hotel room in the Waldorf-Astoria until well into the early hours, five of Mr. Obama’s closest national security advisers, in New York for the administration’s first United Nations General Assembly, went back and forth on what they would advise their boss when they took him the news in the morning. A few hours later, in a different hotel room, they met with Mr. Obama and his senior national security adviser, Gen. James L. Jones, to talk strategy.

The White House essentially decided to outflank the Iranians, to present to their allies and the public what they believed was powerful evidence that there was more to the Iranian site than just some pilot program. They saw it as a chance to use this evidence to persuade other countries to support the case for stronger sanctions by showing that the Iranians were still working on a secret nuclear plan.