Iran and world powers agreed in talks to a more in-depth meeting in Baghdad on May 23 where, Western nations warned Tehran, hard work needed to be done to ease fears it wants the bomb.
EU foreign policy chief Catherine Ashton said there had been "constructive and useful" talks with Iranian chief negotiator Saeed Jalili and said this was a "process which, if it is to be successful, will have to be sustained."
"I have been very clear in my discussions with Dr. Jalili, and he has understood and agreed, that we are looking for the next meeting to take us forward in a very concrete way," she told reporters.
The talks in Istanbul involved the so-called P5+1 grouping - the United States, Russia, China, Britain, France and Germany - and Iran.
The UN Security Council has imposed four rounds of sanctions on Iran because of suspicions that its civilian nuclear programme is a cover for a secret atomic weapons drive, a charge Iran vigorously denies.
The international community's main concern, particularly for Iran's arch foe Israel, is Tehran's growing capacity to enrich uranium, which can be used for peaceful purposes but, when purified further, for a nuclear weapon.
Echoing Ashton, other Western countries stressed the need for the Baghdad discussions to get to the core of the international community's almost decade-old standoff with the West over its nuclear programme.
The White House hailed the "positive attitude" from Iran and world powers - but Deputy National Security Adviser Ben Rhodes reiterated Washington's call for Tehran to take "concrete steps".
British Foreign Secretary William Hague was also cautious, saying in a statement the Istanbul talks "were a first step towards that objective, but there is still a long way to go."
"We now need agreement on urgent, practical steps to build confidence around the world that Iran will implement its international obligations and does not intend to build a nuclear weapon," he added.
France took a similar position.
"Iran has to make urgent and concrete gestures to establish confidence," French Foreign Minister Alain Juppe said in a statement issued in Paris.
Jalili for his part praised the "desire of the other side for dialogue and cooperation. We consider that as a positive sign... For the Iranian people the language of threat and pressure doesn't work."
The last time Iran met with the P5+1 in Istanbul in January 2011, it quickly became apparent the talks would go nowhere.
This time however, diplomats said Tehran's delegation had come with a much more constructive attitude.
"What was very striking as soon as Jalili started talking was that there was a difference in tone, in mood," one envoy said, seeing in this a "clear sign that Iran... wants to get into a serious process."
Of special concern has been Iran's formerly secret Fordo site in a mountain bunker near the holy city of Qom which is enriching to 20 per cent purity but, experts say, could be reconfigured to produce 90-per cent weapons-grade material.
Fordo's expansion - and a major UN atomic agency report in November on alleged "weaponisation" efforts - have led to tighter EU and US sanctions on Iran's oil sector, due to bite this summer, as well as talk of Israeli military strikes.
Whether a second round of talks would succeed remains to be seen, however. Iran is likely to insist on the right to a peaceful nuclear programme while demanding sanctions be eased.
What happened Saturday "cannot be called a breakthrough. If there is a breakthrough, it would come at the next meeting," said Bruno Tertrais, senior research fellow at the Foundation for Strategic Research in Paris.
"It is only when both sides have agreed on the next steps... and when whatever Iran will agree to can be verified, that we will be able to say for certain that something real has happened.
"Until then it's only talk," he said.
US President Barack Obama, seeking re-election in November, in particular is wary of accusations that he has been duped by empty Iranian promises that just buy Tehran more time to inch closer to getting the bomb.
At the same time all parties in the talks, not least energy-hungry China, want the crisis resolved in order to bring down oil prices to help the stuttering global economy.
In a reminder, however, of Tehran's enmity towards Washington, a source close to Iran's delegation said they had spurned a request from their US counterparts for what would have been a rare bilateral meeting on the sidelines in Istanbul.