Iranian foreign minister Mohammad Javad Zarif, who also had an unexpected one-to-one meeting with US secretary of state John Kerry at the UN, said six world powers and Iran had agreed to fast-track nuclear negotiations, with the hope of reaching a deal within a year.
Iran said it was eager to dispel suspicions it was trying to develop a nuclear weapon and to get punishing international sanctions lifted as fast as possible.
Iran, the five permanent members of the UN Security Council and Germany also agreed to hold a new round of substantive nuclear negotiations next month in Geneva, Switzerland.
Mr Zarif said: "We agreed to jump-start the process so we could move forward with a view to agreeing first on the parameters of the end game and move towards finalising it hopefully within a year's time."
Mr Kerry said he was struck by a "very different tone" from Tehran after their sessions, which marked the highest-level direct contact between the US and Iran in six years.
But, like his European colleagues, he stressed a single meeting was not enough to assuage international concerns Iran is seeking to develop nuclear weapons under cover of a civilian atomic energy programme.
Mr Zarif and Mr Kerry sat next to each other at a U-shaped table during the group talks. EU foreign policy chief Catherine Ashton suggested the two men had shaken hands and been cordial with each other.
Foreign Secretary William Hague said there had been a "big improvement in the tone and spirit" from Iran.