“There’s no question in my mind that we are closer now, as we leave Geneva, than when we came,” Mr. Kerry said. “It takes time to build confidence between countries that have really been at odds with each other for a long time now.”

The proposal under consideration in Geneva was to have been the first stage of a multipart agreement. It called for Iran to freeze its nuclear program for up to six months to allow negotiations on a long-term agreement without the worry that Iran was racing ahead to build a bomb. In exchange, the West was to have provided some easing of the international sanctions that have battered Iran’s economy.

After years of off-again, on-again talks, the deal would have been the first to brake Iran’s nuclear program.Despite the diplomats’ insistence on progress, the failure to clinch an agreement raised questions about the future of the nuclear talks, given the fierce criticism that the mere prospect of a deal whipped up in Israel and among Republicans and some Democrats in Congress.

The announcement was a deflating end to a long day of diplomatic twists and turns, after Mr. Kerry huddled for hours with Mr. Zarif and Mr. Fabius to try to close gaps on issues like curbing Iran’s enrichment program and what to do about the heavy-water reactor Iran is building near the city of Arak, which will produce plutonium.

Daryl Kimball, the executive director of the Arms Control Association, said the plant could be dealt with in a future phase of the talks because it would take a year for it to be completed and even longer for it to produce plutonium that could be extracted for a bomb.

But Mr. Kerry said during his recent visit to Israel that the United States was asking Iran, as part of an interim accord, to agree to a “complete freeze over where they are today,” implying that Iran’s plutonium production program would be affected in some way as well. And in a news conference at the end of the talks, Mr. Kerry made clear that limits on the Arak reactor should be part of an initial agreement.

Under a compromise favored by some American officials, Iran might agree to refrain from operating or fueling the facility during the six months the interim accord might last, while continuing construction of the installation.