GENEVA — Two days of marathon negotiations, by far the most direct and extended high-level contact between the United States and Iran in more than three decades, ended early Sunday without agreement on an interim plan on Iran’s disputed nuclear program.

After a tumultuous day of bargaining, diplomats emerged after midnight to acknowledge they had fallen short of a deal that would have required Iran to suspend key parts of its nuclear program in exchange for modest relief on economic sanctions. The sides will try again Nov. 20.

Secretary of State John F. Kerry, who had flown to Geneva at the eleventh hour to try to close a deal, said at a late-night news conference that the talks between Iran and six major powers had been “very productive” and that all sides were determined to continue the efforts.

“We came to Geneva to narrow the differences, and I can tell you without any reservations, we made significant progress,” Kerry said.

“It takes time to build confidence between countries that have really been at odds with each other for a long time now,” he said.

Although a deal had appeared nearly certain a few hours earlier, the talks stalled over technical issues, including details of nuclear concessions required of Iran, and the incentives the Islamic Republic would receive in return. Among the obstacles were disagreements between France and other members of the six-nation bloc known as the P5-plus-1.

Kerry, in a taped interview with NBC’s “Meet the Press,” that airs Sunday, downplayed the differences between Western governments that emerged on the final day of the talks. “A number of nations – not just the French, but ourselves and others – wanted to make sure that we had the tough language necessary, the clarity in the language necessary to be absolutely certain that we were doing the job and not granting more or doing something sloppily that could wind up with a mistake,” He said.

He forcefully rejected accusations that the deal offered to Iran would have endangered Israeli and other allies in the region by allowing Iran to retain some of its civilian nuclear capabilities. “We are not blind, and I don’t think we’re stupid,” Kerry said. “I think we have a pretty strong sense of how to measure whether or not we are acting in the interests of our country and of the globe, and particularly of our allies like Israel and Gulf states and others in the region.”

Kerry added: “We are absolutely determined that this would be a good deal, or there’ll be no deal. Now, that’s why it’s hard.”

Iran’s chief negotiator, Foreign Minister Mohammad Javid Zarif, gave an upbeat assessment as the talks broke up early Sunday.

“What I was looking for was the political determination, willingness and good faith and readiness in order to end this,” said Zarif, appearing at the podium with the European Union’s foreign policy chief, Catherine Ashton. “I think we’re all on the same wavelength, and that’s important. And that gives us the impetus to go forward when we meet again next time.