US Secretary of State John Kerry met Iranian Foreign Minister Mohammad Javad Zarif.
Diplomats from the P5+1 group - China, Russia, Britain, France and Germany - were also present at the talks.
They agreed to hold substantive talks on the issue in the Swiss city of Geneva, beginning on 15 October.
Following the meeting, 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'
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Analysis
image of James Reynolds
James Reynolds
BBC Iran correspondent
In recent years, the travelling brigade of nuclear negotiators has seen much of the world. Air miles aside, they have achieved almost nothing of substance. Diplomats have held talks in Geneva, Istanbul, Baghdad, Moscow, and Almaty. The most recent meeting was in Kazakhstan's biggest city in April 2013.
At times it has been hard to describe the nuclear talks as actual negotiations. More accurately, they have often resembled parallel monologues. But the P5+1 is meeting a new Iranian team.
Iran's newly appointed Foreign Minister, Mohammad Javad Zarif, replaces Saed Jalili as chief negotiator. Mr Zarif will report directly to Iran's President Hassan Rouhani - himself a former nuclear negotiator.
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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".
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
US Secretary of State John Kerry said there had been a "change in tone" from Iran
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 - the five permanent members of the UN Security Council, plus Germany.
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.
'Moderate course'
Hassan Rouhani: "The indefinite possession of nuclear weapons cannot be tolerated"
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.
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