US Secretary of State John Kerry met Iranian Foreign Minister Mohammad Javad Zarif on Thursday.
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, Kerry said he was pleased that 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 program, BBC reported.
"One meeting and a change in tone, which was welcome, doesn't answer those questions yet," he said.
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."
Zarif insisted Iran's nuclear program 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.
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 Rouhani's election in June, Iranian officials have reached out to the West, saying they want to address concerns over Iran's nuclear program.
On Tuesday, 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.
Hassan Rouhani: "The indefinite possession of nuclear weapons cannot be tolerated"
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.
Rouhani has said he is fully empowered by Leader of the Islamic Revolution Ayatollah Seyyed Ali Khamenei to negotiate on the issue.
Iran and the P5+1 have held several rounds of talks on a range of issues, with the main focus being on Tehran’s nuclear energy program.
The two sides wrapped up their latest round of negotiations in April in the Kazakh city of Almaty. An earlier meeting was held in Almaty in February.
The United States, Israel, and some of their allies have repeatedly accused Iran of pursuing non-civilian objectives in its nuclear energy program and have used the unfounded accusation as a pretext to impose illegal sanctions on the Islamic Republic.
Iran rejects the allegations, arguing that as a committed signatory to the nuclear Non-Proliferation Treaty (NPT) and a member of the International Atomic Energy Agency (IAEA), it has the right to use nuclear technology for peaceful purposes.
In addition, the IAEA has conducted numerous inspections of Iran’s nuclear facilities but has never found any evidence showing that Iran’s civilian nuclear program has been diverted to nuclear weapons production.
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