"It is clear that we both want to make progress, and that there is some common ground," European Union foreign policy chief Catherine Ashton, who is formally leading the talks, told reporters.
"However, significant differences remain. Nonetheless, we do agree on the need for further discussion to expand that common ground."
Envoys said they will meet again next month in Moscow after negotiations stretched out for extra hours.
At the heart of the dispute is Iran's insistence that it has the right to enrich uranium and that economic sanctions should be lifted before it stops activities that could lead to its achieving the capability to make nuclear weapons.
Western powers insist Tehran must first shut down enrichment activities before sanctions can be eased.
But both sides have powerful reasons not to abandon diplomacy. The powers want to avert the danger of a new Middle East war raised by Israeli threats to bomb Iran, while Tehran also wants to avoid a looming Western ban on its oil exports.
"We will maintain intensive contacts with our Iranian counterparts to prepare a further meeting in Moscow," Ashton said.
The next meeting, the third in the latest round of talks that began in Istanbul last month, will be held in Moscow on June 18-19.
Ashton leads the negotiations for the six-country group made up of the five permanent members of the U.N. Security Council - Britain, China, France, Russia and the United States - which together with Germany is known as the P5+1.
"Talks were intensive and long," said Iranian chief negotiator Saeed Jalili. "They were detailed, but are left unfinished."
While there was little if any concrete progress, the fact that the two sides agreed to continue talks was a sign of progress in itself, after more than a year of not meeting at all before the latest round of negotiations began in April.
"The two sides' commitment to diplomacy in the absence of any clear agreement is a positive sign," said Ali Vaez, Iran expert at the International Crisis Group think-tank.