Such an accord is aimed at killing off once and for all worries that Iran might develop nuclear weapons under the guise of its civilian programme, and silence talk of war.
Iran denies seeking the bomb and wants the lifting of all UN and Western sanctions, which have caused it major economic problems.
The five permanent members of the UN Security Council plus Germany have been negotiating almost constantly for months, but the talks have come up against major problems — as expected.
US Secretary of State John Kerry and the foreign ministers of Britain, France and Germany arrived Sunday in Vienna seeking to press Iran to make key concessions.
The European ministers left late Sunday however saying no breakthrough had been made, although Kerry remained for further discussions with his Iranian counterpart Mohammad Javad Zarif.
Russia and China sent only lower-ranking officials, with Chinese Deputy Foreign Minister Li Baodong urging both sides "to show flexibility".
Kerry said on arrival that "very significant gaps" remained, while Iranian negotiator Abbas Araqchi said that on all the important issues, no narrowing of positions was evident.
Germany's Foreign Minister Frank-Walter Steinmeier, who like the others held one-on-one talks with Zarif, was the most downbeat, warning that "the ball is in Iran's court".
"It is now up to Iran to decide to take the path of cooperation … I hope that the days left will be enough to create some reflection in Tehran," he said.
Britain's William Hague said that no "decisive breakthrough" was achieved and that there remained a "huge gap" on the key issue of uranium enrichment — an activity that can produce fuel for the country's sole nuclear plant or, if further enriched, the matter for an atomic bomb.
The six powers want Iran to reduce dramatically the scope of its enrichment programme, while Tehran wants to expand it.
Israel, the Middle East's sole if undeclared nuclear weapons state and which together with Washington has refused to rule out military action, is opposed to any enrichment by Iran.
Israeli Prime Minister Benjamin Netanyahu warned Sunday that any nuclear deal leaving Iran with the capability to pursue this activity would be "catastrophic".
"It would be a disaster for the United States and for everyone else," he told Fox News, adding that "a bad deal is actually worse than no deal".
Araqchi said: "Concerning enrichment, our position is clear and rational. As the supreme guide said, the enrichment programme has been planned with the real needs of the country in mind, meaning our need to ensure reactor fuel."
On Saturday, Araqchi said Iran was ready to walk away from the talks if the world powers pushed on with "excessive" demands.
If no agreement is reached by next Sunday when a six-month interim accord with Iran runs out, both sides can decide to extend the pact for longer and keep talking.
French Foreign Minister Laurent Fabius said that if a deal was not struck, "we either extend, a so-called rollover, or we will have to say that unfortunately there is no perspective for a deal".
But such an extension is possible only if both sides agree, and the United States in particular is opposed to such a move unless Tehran first offers major concessions.
Hague said Sunday that such a move "will only be discussed if no progress can be made. It is still too early."