* Big powers' foreign ministers join talks
* Nascent compromise on Iran's "right to enrich" uranium
* Fate of Iran's Arak heavy-water reactor remains dispute (Adds Iran negotiator remarks, details)
By Justyna Pawlak and Fredrik Dahl
GENEVA, Nov 23 (Reuters) - Foreign ministers from Iran and six world powers laboured on Saturday to overcome remaining difficulties and clinch a breakthrough deal aimed at allaying Western suspicions over Tehran's atomic ambitions.
With the sides edging closer, U.S. Secretary of State John Kerry and foreign ministers of the five other nations joined the talks with Iran as they entered an unscheduled fourth day.
The demand that Iran stop or slow construction of a reactor that could yield potential bomb material appeared to be the main outstanding problem holding up an agreement.
British Foreign Minister William Hague and Germany's Guido Westerwelle both cautioned that a deal was not yet guaranteed and that there was work still to do.
A senior Iranian negotiator, Deputy Foreign Minister Abbas Araqchi, said the meeting could run into Sunday, even though Kerry is due to travel to London then.
"We hope to reach a result tonight but if we don't ... it is possible that the talks will continue tomorrow as well," he was quoted as saying by ISNA news agency.
"The discussion is over wording, and progress has not been bad," Araqchi said, according to Mehr News Agency.
Hague said there was a "huge amount of agreement" but the remaining gaps were important and the talks remained difficult.
The powers' goal is to cap Iran's nuclear energy programme, which has a history of evading U.N. inspections and investigations, to remove any risk of Tehran covertly refining uranium to a level suitable for bombs.
Tehran denies it would ever "weaponise" enrichment.
Diplomats said a formidable stumbling block in the negotiations, which began on Wednesday, may have been settled with compromise language that does not explicitly recognise Iran's claim to a "right to enrich" uranium but acknowledges all countries' right to their own civilian nuclear energy. [ID:
Refined uranium can be used to fuel nuclear power plants - Iran's stated goal - but also provide the fissile core of an atomic bomb if refined much further.
NOT "A DONE DEAL"
Russian Deputy Foreign Minister Sergei Ryabkov said Iran's demand to continue construction of the Arak heavy-water reactor that could produce plutonium - an alternative bomb material - remained a tough outstanding issue.
Iran says the Arak plant will only produce medical isotopes.
Germany's Westerwelle told reporters: "It's not a done deal. There's a realistic chance but there's a lot of work to do."
The talks' aim to find a package of confidence-building steps to ease decades of tensions and banish the spectre of a Middle East war over Tehran's nuclear aspirations.
The preliminary pact would run for six months while the powers and Tehran hammer out a broader, longer-term settlement.
Diplomacy was stepped up after the landslide election of Hassan Rouhani, a relative moderate, as Iranian president in June, replacing bellicose nationalist Mahmoud Ahmadinejad.
Rouhani aims to mend fences with big powers and get sanctions lifted. He obtained crucial public backing from Supreme Leader Ayatollah Ali Khamenei, keeping powerful hardline critics at bay.
The draft deal would see Iran suspend some nuclear activities in exchange for the release of billions of dollars in Iranian funds frozen in foreign bank accounts, and renewed trade in precious metals, petrochemicals and aircraft parts.
The United States might also agree to relax pressure on other countries not to buy Iranian oil. Tehran has made clear it wants a more significant dismantling of Western sanctions on its oil exports and use of the international banking system.
France's Laurent Fabius, who objected to what he felt was a one-sided offer to Iran floated at the previous negotiating round on Nov. 7-9, seemed guarded on arrival on Saturday.
"I hope we can reach a deal, but a solid deal. I am here to work on that," he said. France has consistently taken a tough line over Iran's nuclear programme, helping Paris cultivate closer ties with Tehran's adversaries in Israel and the Gulf.
Kerry went to Geneva "with the goal of continuing to help narrow the differences and move closer to an agreement," State Department spokeswoman Jen Psaki said. Direct U.S.-Iranian engagement is crucial to a peaceful solution given the rupture in bilateral ties since Iran's Islamic Revolution in 1979.
As a signatory to the Non-Proliferation Treaty, Iran has always sought recognition of its "right to enrich" uranium, but Western powers say that is not enshrined in the NPT.
Diplomats said revised wording did not explicitly recognise a right to produce nuclear fuel. "If you speak about the right to a peaceful nuclear programme, that's open to interpretation," a diplomat said.
However, Iranian Foreign Minister Mohammad Javad Zarif said: "Enrichment in Iran will not stop and ... enrichment will be a part of any agreement."
European Union foreign policy chief Catherine Ashton, who is coordinating the talks with Iran on behalf of the six nations, held "intensive discussions" with Zarif throughout Saturday and later briefed the other foreign ministers about their talks.
For the powers, an interim deal would mandate a halt to Iran's enrichment of uranium to a purity of 20 percent - a major step towards the bomb threshold, more sweeping U.N. nuclear inspections and a halt to the construction of the Arak reactor.
The OPEC producer rejects suspicions it is covertly trying to develop the means to produce nuclear weapons, saying it is stockpiling nuclear material for future atomic power plants.
Israel says the deal being offered would give Iran more time for to master nuclear technology and amass potential bomb fuel.
Prime Minister Benjamin Netanyahu told local media in Moscow that Iran was essentially given an "unbelievable Christmas present - the capacity to maintain this (nuclear) breakout capability for practically no concessions at all". (Additional reporting by Parisa Hafezi, John Irish, Arshad Mohammed, Louis Charbonneau in Geneva, Katya Golubkova in Moscow, Isabel Coles in Dubai; Editing by Mark Heinrich and Robin Pomeroy)