The talks gained momentum as they hit the Nov. 24 deadline, Mr. Fabius said, allowing world powers to extend the negotiations into the spring of next year. Diplomats said they needed until the end of June 2015 to complete the terms.

They agreed to roll over an interim agreement signed last year that caps some of Iran’s nuclear work in exchange for an easing of Western economic sanctions.

“Talks accelerated in the last period,” Mr. Fabius said. “There is a will to find an agreement I hadn’t felt in the past.

The European Union said Tuesday that its 28 member states had approved extending sanctions relief that Iran won under last year’s interim deal until the new June 30, 2015 deadline for negotiations.