"The French signed off on it, we signed off on it," Kerry said.
Earlier reports said that the talks came apart because France refused to accept the deal with Iran. On Monday, Kerry said the major powers reached an agreement after a marathon bargaining session but Iran wasn't able to accept the deal "at that particular moment."
"There was unity but Iran couldn't take it," he said.
Kerry also said that that Israeli Prime Minister Benjamin Netanyahu's rejection of a deal to limit Iran's nuclear ambitions was premature.
"The time to oppose it is when you see what it is, not to oppose the effort to find out what is possible," Kerry said.
Netanyahu has repeatedly criticized what he considers readiness by the six powers involved in the talks to be too generous to Iran and has aggressively campaigned against an agreement.
But Kerry reasserted the U.S. commitment to Israel, saying the United States would not allow Iran to develop a nuclear bomb.
President Barack Obama, Kerry said, "does what he says," citing the killing of Osama bin Laden and getting American troops out of the wars in Iraq and Afghanistan.
"So believe us on Iran," he said. "He will not bluff."
Kerry said the U.S. has "been meeting constantly" with the Israelis to understand the progress Iran has made in its nuclear program. "We are confident that what we are doing can actually protect Israel more effectively and provide greater security," he said.
Kerry said there is no "end game" in motion and the Geneva talks were a first step in longer process of possible give and take.
Tehran has been eager to reach an agreement to ease international sanctions that have halted most oil exports and crippled the county's economy.
But a key stumbling block has been Iran's insistence that the international community recognize its "right" to enrich uranium as a signer of a U.N. treaty governing the spread of nuclear technology -- also frequently pointing out that Israel has not signed the accord. Kerry's comments challenge the Iranian view, but do not appear to significantly alter the currently Western effort that seeks to curb Iran's ability to make its highest-enrich uranium but possibly leaving intact the country's production of lower-level nuclear fuel.
Iran's highest enrichment level, at 20 percent, is still below the more than 90 percent needed for weapons-grade material, but experts say the process could be done at a rapid pace. Iran insists that its nuclear program is solely for peaceful purposes and that it has no plans to produce a nuclear weapon.
Iran says the 20 percent material is needed for its research reactor, which makes medical isotopes for cancer treatment and other applications. Iran also produces lower level nuclear fuel for its energy-producing reactor, which requires 3.5 percent enriched uranium.
Iranian state TV reported Monday that an agreement for expanded monitoring had been reached in talks with the U.N. nuclear chief in a deal that could boost wider negotiations over Tehran's atomic program.
Abu Dhabi was Kerry's final stop on a lengthy visit to the Middle East. He interrupted his tour on Friday to rush to Switzerland to take part in the weekend negotiations with Iran. He was expected back in Washington late Monday.
Associated Press writer Brian Murphy in Abu Dhabi contributed to this report.
Copyright 2013 The Associated Press. All rights reserved. This material may not be published, broadcast, rewritten or redistributed.