There was no way to meet the deadline, Mr. Kerry said from the tent, which was designed to defeat eavesdropping. The Iranians, he said, perhaps sensing that the deadline meant a lot in Washington and little in Tehran, were intransigent.

“They were turning our own deadline against us to see if we would give ground,” just to be able to claim that the March 31 date had been met, said one senior official, who would not be identified because of the secrecy surrounding the talks.