GENEVA — A month away from a nuclear deal deadline, U.S. and Iranian diplomats tried to narrow differences over how quickly to ease economic penalties against Tehran and how significantly the Iranians must open up military facilities to international inspections.

American officials described the session as “at times intense.”

The talks between Secretary of State John Kerry and Iranian Foreign Minister Mohammad Javad Zarif lasted six hours, in what officials described as the most substantive negotiating round since world powers and Iran clinched a framework pact in April.

Last month’s agreement left big questions, which weeks of subsequent technical discussions have done little to resolve. It was unclear how much progress Kerry and Zarif made before the Iranian delegation began leaving for Tehran.

Asked about completing the full accord by June 30, Zarif said, “We will try.”

His deputy, Abbas Aragchi, said lower-level officials would meet again in Vienna next week.

U.S. officials provided hints of what must have been a difficult dialogue, but said the encounter ultimately proved fruitful. American members of the negotiating team were not authorized to discuss publicly the private talks.

World powers believe they have secured Iran’s acquiescence to a combination of nuclear restrictions that would fulfill their biggest goal: keeping Iran at least a year away from bomb-making capability for at least a decade.