Iran insists its nuclear programme is for peaceful energy purposes
Senior US and Iranian officials have met for rare bilateral talks during discussions between world powers and Iran on its nuclear programme.
Undersecretary of State William Burns and Tehran's chief nuclear negotiator, Saeed Jalili, held what were described as "significant" talks in Geneva.
The five permanent members of the UN Security Council, plus Germany, want Iran to halt its enrichment activities.
The talks ended with an agreement to meet again in October, reports say.
Tehran insists it has the right to develop nuclear energy, but the revelation of a second uranium-enrichment facility last week has raised fears that it is trying to develop nuclear weapons.
The Iranian government has said that it will allow inspectors from the International Atomic Energy Agency (IAEA) to view the site, thought to be near Qom, but has not said when the inspections can take place.
The head of the UN nuclear watchdog, Mohamed ElBaradei, said earlier that Iran had been "on wrong side of the law" in hiding the uranium plant.
"Iran was supposed to inform us on the day it was decided to construct the facility. They have not done that," he told CNN-IBN.
But Mr ElBaradei also stressed that the IAEA did not have credible evidence that Iran had an operational nuclear weapons programme.
'Restatement of positions'
Officials from the US, Russia, China, UK, France and Germany began high-level talks with Iranian representatives in Geneva on Thursday.
During the lunch interval, the senior US official taking part in the discussions met separately with the chief Iranian negotiator.
BBC Middle East editor
These talks matter. The crisis over Iran's nuclear ambitions has been smouldering since 2006, but it has started to emit worrying sparks lately.
At the moment it is hard to identify common ground between the two sides, so the meeting needs to establish - at the very least - a way for them to talk constructively to each other.
Diplomats from the Security Council side say the talks will be a failure if they are not the start of a short and relatively sharp political process that addresses international concerns about what exactly Iran is doing.
Underlying the diplomacy are threats. If there's no progress by the end of the year, Iran will face more sanctions - either from the Security Council or from a consortium of the US, France, Britain and their allies. And beyond that are the veiled and no-so-veiled threats of a military attack on Iran's nuclear facilities.
US State Department deputy spokesman Robert Wood refused to reveal details of the talks afterwards, but US diplomats described them as "significant".
Iranian Foreign Minister Manouchehr Mottaki told journalists at UN headquarters in New York that the discussions had been held in a "constructive" atmosphere.
"We hope that the other side will have the same political will and determination," he said.
The BBC's Jon Leyne in Geneva says the Americans seem to want to play up their importance, perhaps as evidence that President Barack Obama's so-called "hand of friendship" is generating a positive response.
Later, Iran's official news agency Irna reported that the representatives of Iran and the six powers had agreed to hold further talks by the end of October.
Western diplomats, however, told the Associated Press news agency that they were still considering whether to hold a follow-up meeting. The previous such talks occurred more than a year ago.
Our correspondent says that overall, the nuclear talks do not seem to have made much progress.
One Western diplomat said that much of the morning session had been spent in a restatement of positions.
Earlier, the Iranian stated broadcaster IRIB reported that Mr Jalili had used "clear and unequivocal" language during the initial discussions.
"The Islamic Republic would by no means be dissuaded of its certain rights," it quoted him as saying.
Mr Jalili had also given a "detailed explanation" of wide-ranging proposals that Iran had submitted to the six powers last month and "emphasised the necessity of complete global disarmament", it added.
Washington says it is focused on engagement, not sanctions. However, at the same time, US diplomats are making clear that the talks with Iran cannot be open-ended, correspondents say.
"This is the first time that we've agreed to sit down with Iran as a full member of the P5+1 discussions," Mr Wood told journalists.
"We're willing to engage in this process but we're not going to do it forever," he said.
Russia recently signalled it might be prepared to soften its opposition to further sanctions. China, which is also a permanent Security Council member, has said such pressure would not be effective.