Each side appeared to tempering anticipation of an imminent agreement after the United States, Russia, China, France, Britain and Germany came close to winning concessions from Tehran in the last round of negotiations two weeks ago.
Policymakers from the six governments have since said an interim accord on confidence-building steps could finally be within reach to defuse a decade-old standoff and dispel the spectre of a wider Middle East war over the Islamic Republic's nuclear ambitions.
British Foreign Secretary William Hague said remaining differences were narrow in the search for an interim deal that essentially would require Iran to limit its contested uranium enrichment programme in exchange for limited relief from sanctions.
"It is the best chance for a long time to make progress on one of the gravest problems in foreign policy," Hague told a news conference in Istanbul.
Russian Foreign Minister Sergei Lavrov said: "We hope the efforts that are being made will be crowned with success at the meeting that opens today in Geneva."
A senior U.S. negotiator was more cautious, telling reporters: "I think we can (get a deal). Whether we will, we will have to see because it is hard. It is very hard ... If it was easy to do, it would have been done a long time ago."
The official, with an eye to prominent sceptics of deal-making with Iran, including Israel and hawks in the U.S. Congress, said the vast majority of sanctions - particularly on Iranian oil exports and banking - would remain intact after any initial pact and Washington would "vigorously" enforce them.
On the other hand, a Western diplomat said there was still a "very high probability" that foreign ministers would return to Geneva this week to try to nail down an agreement in the negotiations, expected to run through Friday.
A second Western diplomat expressed guarded optimism about a deal, but said "the ball is in the Iranian court."
Western governments suspect Iran has enriched uranium with the covert aim of developing the means to fuel nuclear weapons, which Tehran denies. Refined uranium is used to run nuclear power stations - Iran's stated goal - but can also constitute the core of a nuclear bomb, if enriched to a high degree.
Iranian Supreme Leader Ayatollah Ali Khamenei said in a speech as Western negotiators gathered in the Swiss city that Tehran would not step back from its nuclear rights and he had set "red lines" for his envoys in Geneva. By rights, he was alluding to nuclear fuel production on Iranian soil.
He added, according to his official website: "We want to have friendly relations with all nations and peoples. The Islamic system isn't even hostile to the nation of America, although with regards to Iran and the Islamic system, the American government is arrogant, malicious and vindictive."
Khamenei also called Israel a "rabid dog", and criticised France, which spoke out against a draft deal floated at the Nov. 7-9 negotiating round, for "succumbing to the United States" and "kneeling before the Israeli regime". France said the comments were unacceptable.
The U.S. official said Khamenei's remarks were "of course, of concern." He said leaders in Iran and the United States should not engage in rhetoric that deepens mistrust between the two estranged nations, which have not had diplomatic relations for more than three decades.
A senior U.S. State Department official said there would be a bilateral U.S.-Iranian meeting on Thursday. The official did not say who in the U.S. delegation, which is headed by Under Secretary of State for Political Affairs Wendy Sherman, would meet with the Iranians.
Israeli Prime Minister Benjamin Netanyahu flew to Russia to appeal for tougher terms in any accord with Iran after failing to convince the United States that the world powers are pursuing a bad deal.
Israel, assumed to have the Middle East's only nuclear arsenal, sees a nuclear-armed Iran as a mortal threat and wants its arch-enemy's uranium enrichment capabilities dismantled and its enriched uranium stockpile removed.
Israel worries that the initial deal being discussed in Geneva would buy Iran time to pursue nuclear weapons because it would not scrap its nuclear fuel-making infrastructure.
The six powers see it, however, as a way to cap Iran's nuclear activity as a stepping stone towards a broad final settlement that would eliminate any risk of Tehran "weaponising" uranium enrichment.
White House deputy national security adviser Ben Rhodes sought to allay Israeli misgivings, saying negotiators needed the six months that an interim solution would provide to strike a comprehensive agreement.
"We share the end goal and that's the point of these whole negotiations, which is to prevent Iran getting nuclear weapons," he told CNN.
The last meeting stumbled over Iran's insistence that its "right" to enrich uranium be explicitly recognised and over its building of a heavy-water reactor near Arak that could yield plutonium, an alternative bomb ingredient, once operational.
Iranian Foreign Minister Mohammad Javad Zarif has since suggested a way around the first sticking point, saying Tehran has the right to refine uranium but is not now insisting that others recognise that right.
U.S. Secretary of State John Kerry said the issue of whether Iran will be allowed to enrich uranium in the longer term would not be decided in an interim deal.
A United Nation's inspectors' report last week showed Iran had stopped expanding enrichment and had not added major new components at Arak since August, when moderate Hassan Rouhani replaced hardliner Mahmoud Ahmadinejad as president.
Zarif, Tehran's chief nuclear negotiator, said on the eve of the meeting there was "every possibility" of a successful conclusion provided there was good faith and the political will among all involved to resolve problems.
American lawmakers urged President Barack Obama's administration to take a tougher line with Iran.
The talks in Geneva started on Wednesday with a meeting between Zarif and European Union foreign policy chief Catherine Ashton, who coordinates contacts with Iran on behalf of the six powers, before a full plenary meeting of Iran and those nations.
After years of confrontation, a shift towards meaningful diplomacy between Iran and the world powers took shape after Rouhani's landslide election victory on a platform to relieve the Islamic Republic's international isolation and try to lift sanctions, which are strangling Iran's oil-dependent economy.
Rouhani wants action soon: Western sanctions have reduced Iran's daily oil export revenue by 60 percent since 2011 and caused its currency to collapse.
Still, diplomats say Iran has so far refused to meet all of the powers' demands. They include suspending enrichment of uranium to 20 percent fissile purity - a significant advance towards the threshold for bomb fuel - as well as limiting its enrichment capacity and mothballing the Arak reactor project.
Western diplomats have kept many of the details of a preliminary deal under wraps but said this would not win Iran relief from the most painful sanctions on oil trade and banking that many believe finally forced it into serious negotiations.
Under an initial deal the OPEC producer is likely to temporarily regain access to precious metals markets and trade in petrochemicals and could see the release of some of its oil revenues frozen in oversees accounts.
The Iranian assets that would be unfrozen as part of any deal this week would amount to less than $10 billion, U.S. national security adviser Susan Rice told CNN.
* Iran and big powers neared preliminary nuclear deal 10 days ago
* West wants Iran to scale back uranium enrichment
* Iran's Khamenei cites "red lines," open to detente
* Tehran demands quick sanctions relief for ailing economy