While the talks have made progress over the past year, differences on sticking points are still wide enough to potentially prevent an agreement in the end.
France was demanding more stringent restrictions on the Iranians under any deal than the other Western delegations, officials said.
"The great paradox is that Congress and Israel have put the pressure on the Americans instead of pressuring Iran which is what we need to be doing," the official said.
Iran's delegation told the six powers it was returning to Tehran due to the death of President Hassan Rouhani's 90-year-old mother on Friday.
Prior to the Iranian departure, U.S. Secretary of State John Kerry, Energy Secretary Ernest Moniz, Iranian Foreign Minister Mohammad Javad Zarif and Iranian Atomic Energy Organisation chief Ali Akbar Salehi held another series of meetings to break the impasse.
Technical and political experts have also gathered daily to discuss options that could form the basis of an agreement under which Iran would accept curbs on sensitive nuclear work for at least a decade and sanctions on it would be gradually eased.
There was no breakthrough this week. Disagreements arose among the powers, with France insisting on a longer period of restrictions on Iran's nuclear work. It also opposed the idea of suspending some U.N. sanctions relatively quickly if a deal is struck.
Iran, which denies allegations from the Western powers and their allies that it harbors nuclear weapons ambitions, wants all U.N. sanctions to be lifted immediately, including those targeting its nuclear program.
"They insist they have to go immediately. No way. It is out the question," said a senior European negotiator.
Zarif said the talks had reached a "very crucial point" and progress had been made this week. He also suggested the six powers needed to reach a unified position.
"Given that Americans had officially said that further internal coordination meetings needed among the (six) members, the talks were ended and will resume next week in Lausanne," Iran's ISNA news agency quoted Zarif as saying.
Kerry said they made good progress, adding: "We'll be back next week." Russia's chief negotiator Sergei Ryabkov told Reuters he agreed wholeheartedly with Kerry's assessment.
During that meeting, Kerry expressed condolences to the delegation for the passing of Rouhani's mother and greetings for the Iranian new year holiday Norouz, which begins on Saturday.
U.S. President Barack Obama prepared a video message to Iran's people and leaders on Thursday, saying this year represented the "best opportunity in decades" to improve ties between their two countries. But differences in the nuclear talks remained, he said.
Western and Iranian officials have said that the sides are very far apart, though all delegations want a deal.
POLITICAL FRAMEWORK
The Europeans and Kerry plan to meet in London on Saturday before the end-March deadline for a political framework agreement and a full nuclear deal by June 30.
Not all members of the six power group believe March 31 is an important deadline.
"For us the deadline is June 30," the senior European official said.
The London meeting is intended to bridge differences among the Americans and Europeans, negotiators said. Officials have expressed concerns that the French might block a deal.
EU foreign policy chief Federica Mogherini denied there were divisions between Europe and the United States.
"There is unity, there is unity on the fact that we want a deal, we want a good deal," she said in Brussels after talks with French President Francois Hollande, German Chancellor Angela Merkel and British Prime Minister David Cameron.
This week's re-election of Israeli Prime Minister Netanyahu, a fierce opponent of engagement with Iran and critic of a possible nuclear deal, made clear that the pressure on the United States would not let up.
Pressure from the U.S. Congress is also driving the pace of negotiations. Obama bought some time on Thursday after U.S. Senate Democrats and Republicans agreed to delay until April 14 the Senate Foreign Relations Committee's vote on legislation that would force Obama to submit any agreement with Iran for Congress' approval.
Obama has said a nuclear deal does not need Congressional approval and said he would veto any proposals for new U.S. sanctions.
Chinese Foreign Minister Wang Yi told Kerry the talks "must not fall short for lack of a final effort", China's Foreign Ministry said after the two spoke on the telephone.
The biggest sticking point, Western officials said, remains Iran's demands to have no limits on research and development of advanced centrifuges, machines that purify uranium for use in nuclear reactors or, if very highly enriched, in weapons.
Another is the lifting of sanctions. Iran wants all United Nations sanctions and the most crippling U.S. and European Union restrictions on Tehran's energy and financial sectors lifted immediately after a deal is agreed.
A further area of disagreement is the duration of a deal. Obama has said restrictions on Iranian nuclear work should be in place for at least 10 years. U.S. negotiators are pushing to make it longer than that, while France wants it to last for at least 15 years with another decade of intense U.N. monitoring of Iranian nuclear sites.
There are a few areas of tentative agreement, including that Iran could operation around 6,000 early generation centrifuges. But officials close to the talks dismissed reports of a tentative deal, saying they were very far from circulating anything remotely resembling a draft accord.
(Reuters)(Additional reporting by John Irish and Lesley Wroughton; Writing by Louis Charbonneau and Parisa Hafezi; Editing by Giles Elgood)
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