After meeting Iranian officials on Sunday, Javier Solana, the EU's foreign policy chief, said the talks had been worthwhile, and Ali Larijani, Iran's senior nuclear negotiator, said progress was made and that some "misunderstandings" had been removed.
The talks in Vienna – which began on Saturday – have been described as a last-ditch attempt to persuade Iran to halt its nuclear programme before the United Nations security council imposes sanctions on the country.
Solana said the two sides would meet again next week.
Iran has so far resisted requests for it to freeze its nuclear programme and its enrichment of uranium in particular.
Tehran says it has a right to develop nuclear technology for peaceful purposes.
The US and the EU say that Iran is enriching uranium with the intention of building a nuclear weapon.
The EU has offered Iran economic incentives to halt its nuclear programme.
Threat of sanctions
Nicholas Burns, the US undersecretary of state, said on Friday that Washington expected the UN security council to start discussing a draft resolution on sanctions as early as next week, unless Tehran does a last-minute about-turn and agrees to halt enrichment.
But there might be opposition to this from within the security council.
Russia and China have so far resisted a quick move to impose sanctions even though they agree to them as an ultimate punishment if Iran refuses to halt enrichment.
Philippe Douste-Blazy, the French foreign minister, has said that Iran might agree to halt its nuclear programme if it fears that sanctions might spark a domestic backlash.
"Discontent among the Iranian people over the prospect of sanctions could make the regime change tack," Douste-Blazy said in Abu Dhabi as he wrapped up a brief visit to the United Arab Emirates capital on Sunday.
"The regime may fear the reaction of its own public opinion," he told a joint news conference with his UAE counterpart Sheikh Abdullah bin Zayed al-Nahayan.
"If it appreciated the risk of isolation hanging over the country, it would not be ready to pay the price of it."
Arab Persian Gulf countries, Iran's near-neighbours, publicly oppose sanctions or military action against Iran but have privately voiced their fears that Iran is pursing a nuclear weapons programme.