Secretary of State John Kerry met privately on the sidelines of a meeting at the United Nations about Iran's nuclear program with Iran's Foreign Minister Jarvad Zarif, Kerry said.
The meeting came hours after Iranian President Hassan Rouhani urged the destruction of all nuclear weapons.
The Kerry-Zarif meeting was the first official high-level meeting between the U.S. and Iran since the Iranian revolution in 1979.
"We took a moment to explore a little further the possibilities of how to succeed based on what President Obama laid out in his speech to the General Assembly earlier this week," Kerry said. "And so we're agreed to try to continue a process that would make concrete and find a way to answer the questions that people have about Iran's nuclear program."
Delegations from both countries also agreed to meet again with their European and Chinese counterparts next month, European Union High Representative Catherine Ashton told reporters.
Rouhani's statement today on nuclear weapons was closely watched because his country faces severe international embargoes because its nuclear program is suspected of building a nuclear arsenal.
"Any use of nuclear weapons is a violation of the U.N. charter and a crime against humanity," Rouhani said, speaking at U.N. headquarters in New York.
Rouhani, head of the Non-Aligned Movement, called for a total destruction of nuclear weapons and said "de-targeting, de-alerting or reducing the number of nuclear weapons [is] not [a] substitute for their total elimination."
The nuclear weapon states must lead the charge to disarm, Rouhani said, and he called on Israel to join the Non-Proliferation Treaty "without delay" in a rare, direct reference to the country.
"The world has waited too long to disarm," Rouhani said. "As long as nuclear weapons exist, the threat of their use exists."
In his speech, Rouhani laid out the following three-pronged plan to promote disarmament.
He called for an early commencement of negotiations, in the Conference on Disarmament, on a comprehensive convention on nuclear weapons for the prohibition of their possession, development, production, acquisition, testing, stockpiling, transfer, use or threat of use, and for their destruction.
He urged the designation of Sept. 26 as an international day dedicated to eliminating nuclear weapons.
Rouhani also proposed convening a high-level international conference on nuclear disarmament in five years to review progress in this regard.
In advance of the meeting between Kerry and Zarif, who also were to meet in a group with foreign ministers from Russia, China, Britain, France and Germany, the so-called P5+1, the State Department downplayed expectations. Officials said that nobody expected a breakthrough from this one meeting, but that it would open an opportunity to see if the Iranians were serious about wanting to negotiate.
Asked earlier today what he needed to know from the Iranians to show that they were serious, Kerry responded, "I'll let you know after they've been serious."
Kerry added, "We're going to have a good meeting, I'm sure."