Afterwards, the European Union's foreign policy chief, Javier Solana, told reporters that parties had "agreed to intensify dialogue in the coming weeks" and hold further discussions before the end of the month.
He said Iran had told them that it planned to "co-operate fully and immediately" with the International Atomic Energy Agency (IAEA) on the new enrichment facility, and would invite inspectors "soon, we expect in the next couple of weeks".
Mr Solana also said it had been agreed in principle that some low-enriched uranium (LEU) produced in Iran would be sent to a third country for further enrichment and fabrication into fuel for the Tehran research reactor, which produces isotopes for medical applications.
Paul Reynolds BBC News, London
The talks in Geneva seem to have resulted in negotiations reaching a plateau. Whether a ravine lies ahead remains to be seen.
If it isn't so far, so good, then at least it is so far, not worse. The Iranians called the talks productive, though the US Secretary of State Hillary Clinton said she wanted action as well as gestures.
And there has been, if not a breakthrough, then some progress which has averted an immediate confrontation, though Iran is still resisting the main Security Council demand for it to suspend uranium enrichment.
One positive action was Iran's agreement to open up its Qom plant soon. Another was an agreement for the six contact countries to take some of Iran's low-enriched uranium and enrich it further outside Iran, to be used in an IAEA-monitored research reactor producing medical isotopes, useful in imaging and treating cancers. This will reduce Iran's enriched stockpile, but it will go on enriching more.
There was a one-on-one meeting between the Americans and the Iranians as well. Talk of further sanctions will be on hold for the moment, and there should be further negotiations soon. If there can be agreement on a freeze-freeze next (no more centrifuges, no more sanctions), then they are getting somewhere. But is all this prevarication and delay?
The EU envoy noted the significance of the full participation of the United States, particularly the rare bilateral talks between Undersecretary of State William Burns and Tehran's chief nuclear negotiator, Saeed Jalili, during lunch.
At a news conference in Washington later on Thursday, President Obama said the Iranian government had heard a clear and unified message from the international community in Geneva.
"Iran must demonstrate through concrete steps that it will live up to its responsibilities with regard to its nuclear programme," he said.
"In pursuit of that goal, today's meeting was a constructive beginning. But, it must be followed with constructive action by the Iranian government."
Mr Obama said Tehran had to demonstrate its commitment to transparency by granting IAEA inspectors unfettered access to the facility near Qom within two weeks, and then build confidence in the West that its nuclear programme is peaceful.
"We expect to see swift action. We're committed to serious and meaningful engagement, but we're not interested in talking for the sake of talking," he warned.
Iran says the enrichment plant at Qom is not operational yet
"If Iran does not take steps in the near future to live up to its obligations then the United States will not continue to negotiate indefinitely and we are prepared to move towards increased pressure," he added. "Our patience is not unlimited."
Earlier at the United Nations in New York, Iran's foreign minister said the six powers had taken a different approach to the talks, and not reached a "hasty" judgement about Tehran's proposed agenda.
Manouchehr Mottaki said the negotiations in Geneva had been held in a "constructive" atmosphere and expressed hope that the other side would demonstrate political will and determination.
He declared that Iran was prepared to enhance the form of the discussions and raise them to the level of a "summit" meeting.
Mr Mottaki also said Iran had now announced all of its nuclear sites to the IAEA, and defended its right to pursue uranium enrichment.
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