US and European allies have welcomed what they called a "significant shift" in Iran's attitude to its nuclear programme, after high-level UN talks.
US Secretary of State John Kerry said after meeting Iranian Foreign Minister Mohammad Javad Zarif he was struck by the "very different tone".
But Mr Kerry said Iran still had questions to answer.
Substantive talks with Iran on its nuclear programme are due to take place in Geneva from 15 October.
They will involve the five permanent members of the UN Security Council - the US, Russia, Britain, France and China - along with Germany, known as the P5+1.
The US-Iran meeting in New York represented the highest-level direct contact between the countries in six years. Diplomats from the P5+1 were also present.
Mr Kerry said he was pleased that Mr Zarif "put possibilities on the table", but said a lot of work remained to be done and that Iran would have to answer questions about its nuclear programme.
"One meeting and a change in tone, which was welcome, doesn't answer those questions yet," he said.
'Nothing but peaceful'
Mr Zarif called the talks "constructive" and said the diplomats had made progress on resolving international issues in a manner that respected the rights of the Iranian people.
"I am satisfied with this first step," he said. "Now we have to see whether we can match our positive words with serious deeds so we can move forward."
Mr Zarif insisted Iran's nuclear programme was "nothing but peaceful" and pledged to prove it to the international community.
The Iranian foreign minister called sanctions against Iran "counterproductive" and added he hoped all bilateral, unilateral and multilateral sanctions would be lifted in the near future.
Likewise, British Foreign Secretary William Hague said afterwards the tone and spirit of the meeting were "extremely good".
European Union foreign policy chief Catherine Ashton said there was an agreement to "go forward with an ambitious timeframe".
However, Iran's new envoy to the International Atomic Energy Agency, Reza Najafi, expressed caution on Friday, saying: "This is the first meeting, so nobody I guess should expect that in just one day we can solve our problems."
New Iranian President Hassan Rouhani has said he wants to reach a deal on the nuclear dispute in three to six months.
But the Americans have said there will be no major concessions on sanctions until the Iranians take concrete steps to reassure the world they are not seeking nuclear weapons.
Iran reaches out
Earlier, President Rouhani told the UN General Assembly that no country should possess nuclear arms.
Iran has been negotiating over the nuclear issue since 2006 with the P5+1.
Since Mr Rouhani's election in June, Iranian officials have reached out to the West, saying they want to address concerns over Iran's nuclear programme.
On Tuesday, Mr Rouhani told the General Assembly that he was prepared to engage in "time-bound and results-oriented" talks.
On Thursday, he called for stricter controls on nuclear weapons as part of a global effort to eventually rid the world of them.
"No nation should possess nuclear weapons, since there are no right hands for these wrong weapons," he said, speaking on behalf of the Non-Aligned Movement at the General Assembly.
The P5+1 have asked Iran to halt production and stockpiling of uranium enriched to 20% - a step away from achieving a nuclear weapons capability.
They also demanded Iran shut down the Fordo underground enrichment facility.
In return, they offered to ease the sanctions that have severely affected Iran's economy.
US President Barack Obama has welcomed the new Iranian president's more "moderate course".
He told the UN on Tuesday that the US wanted to resolve the nuclear issue peacefully, but was determined to prevent Iran from developing a nuclear weapon.
Mr Rouhani has said he is fully empowered by Iran's Supreme Leader Ayatollah Khamenei to negotiate on the issue.
The BBC's Bridget Kendall, who is at the UN, says President Rouhani has signalled a sharp departure from the foreign policy and the tone of his predecessor, Mahmoud Ahmadinejad, whose bombastic pronouncements at the UN in the past resulted in walk-outs.