The United States, Britain, France, Germany, Russia and China want Iran to reduce its nuclear fuel-making capacity to deny it any means of quickly producing atom bombs. In exchange, international sanctions that have crippled the large OPEC member's oil-dependent economy would gradually be lifted.
Iran says it is enriching uranium for peaceful energy purposes only and wants the sanctions removed swiftly. But a history of hiding sensitive nuclear work from U.N. inspectors raised international suspicions and the risk of a new Middle East war if diplomacy fails to yield a long-term settlement.
"Obviously we have some very significant gaps still, so we need to see if we can make some progress," Kerry said ahead of meetings with foreign ministers who flew into the Austrian capital at the weekend to breathe new life into the talks.
Iranian Deputy Foreign Minister Abbas Araqchi delivered a similar message. He was quoted by Iran's Arabic language al-Alam television as saying that "disputes over all major and important issues still remain. We have not been able to narrow the gaps on major issues and it is not clear whether we can do it."
Kerry arrived in Vienna in the early hours after clinching a deal in Kabul withAfghanistan's presidential candidates to end the country's election crisis.
"It is vital to make certain that Iran is not going to develop a nuclear weapon and that their program is peaceful and that's what we're here to try and achieve and I hope we can make some progress," Kerry said in Vienna.
German Foreign Minister Frank-Walter Steinmeier told reporters that Germany and the other members of the six-power group have tried to persuade Iran of the urgency of a deal.
"This may be the last chance for a long time to peacefully resolve the dispute over Iran's nuclear program," he told reporters. "It's now up to Iran to decide whether it wants cooperation with the international community or to remain in isolation. ... The ball is inIran's court."
British Foreign Secretary William Hague said it was crucial for Tehran "to be more realistic about what is necessary" to reach a nuclear deal, adding that no breakthroughs had been achieved and there was "no major change in the state of play in these negotiations as of this moment".
Kerry also met Iranian Foreign Minister Mohammad Javad Zarif, though no readout was immediately available. On Saturday, a senior U.S. officialsaid Iran was sticking to "unworkable and inadequate" positions.
Neither pessimistic nor optimistic
Another of Kerry's meetings on Sunday was with Germany's Steinmeier, who raised new accusations of U.S. spying on Berlin.
Steinmeier told reporters that in the meeting with Kerry he called for "reviving this (U.S.-German) relationship, on a foundation of trust and mutual respect." Kerry referred to theUnited States and Germany as "great friends."
Germany asked the CIA station chief in Berlin last week to leave the country following fresh charges of U.S. spying on Berlin. Kerry and Steinmeier were expected to hold a joint news conference later on Sunday.
Kerry, Steinmeier and their British and French counterparts also discussed the escalation of hostilities between Israel and Palestinian militants in the Gaza Strip.
Araqchi said that he was "not pessimistic but also not very optimistic" about the chances for an agreement with the sextet ahead of the self-imposed deadline of July 20. "No proposal has been accepted yet. We have not reached any agreement over the enrichment (program of Iran) and its capacity."
He added that if the talks collapsed, Iran would resume higher-level enrichment that it suspended on Jan. 20 when a preliminary accord the sides struck two months before took effect. Iran won limited relief from sanctions in return.
The Nov. 24 deal included a provision for lengthening talks on a permanent agreement by up to six months if all sides agree. Araqchi said "there is a possibility of extending the talks for a few days or a few weeks if progress is made."
A senior U.S. official said on Saturday that an extension would be difficult to consider without first seeing "significant progress on key issues".
French Foreign Minister Laurent Fabius also raised the possibility of extending the talks.
"If we can reach a deal by July 20, bravo, if it's serious," he told reporters. "If we can't, there are two possibilities. One, we either extend ... or we will have to say that unfortunately there is no prospect for a deal."
Failure to seal a deal would mean the limited sanctions relief currently in place for Iran would end and Tehran could expect tougher sanctions, above all from the United States.
Iran says it is refining uranium to low levels of fissile purity to fuel a planned network of nuclear power stations. It earlier described its higher-level - or 20 percent purity - enrichment as material to fuel a medical research reactor. High-enriched uranium - or 90 percent - is for nuclear weapons.
The Russian and Chinese foreign minister were not in Vienna on Sunday due to a meeting in Brazil of the BRICS developing countries. Moscow and Beijing sent senior diplomats to Vienna instead. (Additional reporting by Parisa Hafezi, Fredrik Dahl and Louis Charbonneau; Writing by Louis Charbonneau;