* U.S. wants first step from Iran to curb nuclear activity
* Iran says deal possible, but talks will be very difficult
* Israel warns of "mistake of historic proportions"
* Higher-grade enrichment at centre of negotiations
(Adds details, background, Netanyahu comment)
GENEVA, Nov 7 (Reuters) - Iran and six world powers are making progress in negotiations aimed at ending a decade-long stand-off over its nuclear ambitions but the discussions are "tough", Tehran's foreign minister said on Thursday.
Mohammad Javad Zarif made the comment to Reuters after a first session in the two-day talks in Geneva that seek to build on a diplomatic opening from Tehran after the June election of Hassan Rouhani, a relative moderate, as president.
The powers hope to reach a "first step" deal to allay concerns about Tehran's nuclear programme - which the West fears may be aimed at developing a nuclear weapons capability - though both sides say a breakthrough is far from certain.
Israel, Iran's arch-enemy, made clear it did not like the proposals under discussion in Geneva, describing them as potentially "a mistake of historic proportions".
Iran says it is enriching uranium solely for peaceful nuclear energy and wants the powers to start lifting harsh sanctions severely damaging the OPEC producer's economy.
Both sides have limited leeway for compromise, with hardliners in Iran and in Washington likely to denounce any concession they regard as going too far.
"The talks went well," Zarif told Reuters after the morning session between Iran, the United States, Britain, France, Germany, Russia and China. "I'm hopeful that we can move forward. We are making progress, but it's tough."
Iranian Deputy Foreign Minister Abbas Araqchi said he hoped a deal could be struck but that the sides remained far apart.
"The differences are widespread and deep. This is undeniable. And continuing the negotiations will not be an easy task, but this does not cause us to lose hope," he said, and he remained hopeful a "final understanding" could be reached.
A spokesman for European Union foreign policy chief Catherine Ashton, who is coordinating talks with Iran on behalf of the powers, described the morning session as "good" but declined to give details.
Michael Mann also said discussions would continue in smaller groups in the afternoon before Ashton and Zarif, who also had a breakfast meeting, were due to meet again.
"The talks are extremely complex and they are now getting into a serious phase. We very much hope there will be concrete progress here in the next couple of days," he told reporters.
ROLLING BACK NUCLEAR PROGRAMME?
The United States and its allies say they are encouraged by Tehran's shift to conciliatory rhetoric since the election of Rouhani. After years of deepening hostility that raised fears of another Middle East waR, Rouhani has promised to try to repair ties with the West and secure relief from sanctions.
But the Western allies say Iran must back its words with action and take concrete steps to scale back its atomic work.
"What we're looking for is a first phase, a first step, an initial understanding that stops Iran's nuclear programme from moving forward and rolls it back for the first time in decades," a senior U.S. official said on the eve of the talks.
That would help buy time needed for the Islamic Republic and the powers to reach a broader diplomatic settlement and avert any descent into another Middle East conflagration that would destabilise the global economy.
The six nations want Iran to suspend its most sensitive uranium enrichment efforts, reduce its stockpile of such material and diminish its capacity to produce it in the future.
In return for any concessions, Iran wants the powers to lift the sanctions that have slashed its oil revenues by 60 percent since 2011 and cut the value of its currency in half.
The exact nature of a possible first step remain unclear. But the six nations are unlikely to agree on anything less than a suspension of enrichment of uranium to 20 percent fissile purity, a level that constitutes a major milepost on the way to producing fuel for a nuclear warhead.
The U.S. official said Iran at this stage must address important aspects of its nuclear activity, including more rigorous U.N. inspections. Iran's construction of a research reactor near the town of Arak is also a growing concern for the West because of its potential to yield plutonium for bombs.
A senior aide to a U.S. senator briefed by the White House and State Department said Washington would offer to work with Iran in a six-month confidence-building period. During that time Washington would offer Tehran, among other things, relaxed restrictions on Iranian funds held in overseas accounts.
In exchange, Iran would stop enriching uranium to 20 percent and convert its existing stockpile of 20 percent uranium to an oxide form suitable for processing into reactor fuel, and take other measures to slow the programme.
It would also limit the number of centrifuges used for lower-level enrichment, forgo the use of advanced centrifuges - which refine uranium 2-3 times as fast - and not commence operation of the Arak reactor, the aide said.
The U.S. House of Representatives overwhelmingly passed a new sanctions bill in July that aims to reduce Iran's oil exports to a trickle in a year. The Senate's banking panel had been expected to introduce its version of the bill in September, but the Obama administration has pushed it to delay the new legislation in order to give the Geneva talks a chance.
Western diplomats involved in the talks are hesitant to divulge specifics about the discussions due to sensitivities involved. But Israeli Prime Minister Benjamin Netanyahu said he disliked the outlines of a preliminary deal emerging in Geneva.
"Israel understands that there are proposals on the table in Geneva today that would ease the pressure on Iran for concessions that are not concessions at all. This proposal would allow Iran to retain the capabilities to make nuclear weapons," he said in a speech.
"Israel totally opposes these proposals. I believe that adopting them would be a mistake of historic proportions. They must be rejected outright."
Widely assumed to be the Middle East's only nuclear power, Israel views Iran as a threat to its existence and has warned it could launch pre-emptive strikes against Iranian nuclear sites if diplomacy fails to stop the programme.
(Additional reporting by Justyna Pawlak and Fredrik Dahl in Geneva, Timothy Gardner in Washington,; Marcus George in Dubai; Editing by Mark Heinrich)