* Possible compromise on Iran's claimed "right to enrich" uranium
* Kerry, Lavrov, Fabius and Hague to join high-stakes talks
* Iranian chief negotiator sees "considerable progress"
* Fate of Iran's Arak heavy-water reactor remains at issue
* Israel renews campaign of criticising offer to Iran (Adds French, UK foreign ministers to attend talks, Israeli PM quote)
By Louis Charbonneau and Parisa Hafezi
GENEVA, Nov 23 (Reuters) - U.S. Secretary of State John Kerry will join talks on Iran's nuclear programme in Geneva on Saturday, as Tehran and six world powers appeared to be on the verge of an elusive breakthrough in the decade-old dispute.
The French and British foreign ministers, Laurent Fabius and William Hague, were also due to take part in intense negotiations on a deal under which Iran would curb its atomic activity in exchange for some sanctions relief.
The announcements came after diplomats in the Swiss city said a major sticking point in the talks, which began on Wednesday, may have been overcome.
Kerry would leave for Geneva later on Friday "with the goal of continuing to help narrow the differences and move closer to an agreement," State Department spokeswoman Jen Psaki said.
The decision was taken after consulting with European Union foreign policy chief Catherine Ashton, who is coordinating talks with Iran on behalf of the six powers, Psaki said.
Later, deputy State Department spokeswoman Marie Harf said that Kerry decided to travel to Geneva "in light of the progress being made" and with "the hope that an agreement will be reached."
Russian Foreign Minister Sergei Lavrov arrived in Geneva on Friday evening and met with Iranian Foreign Minister Mohammad Javad Zarif and with Ashton, a Russian spokeswoman said.
Fabius was expected to arrive early on Saturday, a diplomatic source said, and Hague said in a Twitter message that he would also attend the meeting.
Diplomats earlier said a compromise over Iran's insistence that its "right" to enrich uranium be internationally recognised has been proposed, possibly opening the way to a long-sought breakthrough.
Fabius expressed hope that a deal could be made. France has taken a harder line than other Western powers and repeatedly urged the six-power group not to make too many compromises with Tehran.
"You know our position ... it's a position based on firmness, but at the same time a position of hope that we can reach a deal," Fabius said in Paris.
The United States and other Western powers say there is no such thing as a right to enrich - a process that can yield both electricity and nuclear bombs - but Iran views it as a matter of national sovereignty and crucial to any deal that would resolve the standoff over its nuclear intentions.
The Islamic Republic also wants relief from economic sanctions in return for any nuclear concessions it makes that could allay the West's suspicions that its nuclear fuel-making programme has military rather than its stated civilian goals.
Foreign ministers from the six nations negotiating with Iran - the United States, Russia, China, France, Britain and Germany - waded into the previous talks on Nov. 7-9 and came close to winning concessions from Iran, which they count on to reduce the risk of Iran achieving a nuclear weapons capability.
POLITICALLY CHARGED DETAILS
In the days running up to the talks, policymakers from the six powers said an interim accord on confidence-building steps could be within reach to start a cautious process of detente with Iran and banish the spectre of a wider Middle East war.
Under discussion is Iranian suspension of some sensitive nuclear activities, above all medium-level uranium enrichment, in exchange for sanctions relief. That could involve releasing some Iranian funds frozen in foreign bank accounts and allowing 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 more significant diluting of the sanctions blocking its oil exports and its use of the international banking system.
Diplomacy on Tehran's nuclear aspirations has revived remarkably since the election of Hassan Rouhani, a relative moderate, as president in June on promises of winning sanctions relief and diminishing Iran's international isolation.
The sides have struggled to wrap up a deal, bogged down in politically vexed details and hampered by mutual mistrust.
Diplomats said new, compromise language being discussed did not explicitly recognise a right to produce nuclear fuel by any country. "If you speak about the right to a peaceful nuclear programme, that's open to interpretation," a diplomat told Reuters without elaborating.
No other details were available, but Zarif, Tehran's chief negotiator, said earlier in the day that significant headway had been made even though three or four "differences" remained.
The fate of Iran's Arak heavy-water reactor project - a potential source of an alternative bomb material, plutonium - and the extent of sanctions relief were among the other stumbling blocks, diplomats said.
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.
SENATE SANCTIONS PUSH
A senior European diplomat told reporters earlier that foreign ministers of the six states would come to Geneva only if there was a deal to sign. "We have made progress, including core issues," the diplomat said.
Zarif and Ashton met throughout the day on Friday to try to narrow the remaining gaps.
Israel continued its public campaign of criticising the offer of sanctions rollbacks for Iran, voicing its conviction that all it would achieve would be more time for Iran to master nuclear technology and amass potential bomb fuel.
"I think right now the international community ... has all the leverage to roll back its (Iran's) nuclear making capacities," Israeli Prime Minister Benjamin Netanyahu told Channel Rossia in Moscow
"It's a pity, just when they have this maximum leverage, that they're backing off and essentially giving Iran an unbelievable Christmas present - the capacity to maintain this breakout capability for practically no concessions at all," he said.
For the powers, an interim deal would mandate a halt to Iran's enrichment of uranium to a purity of 20 percent - a major technical step towards the bomb threshold, more sweeping U.N. nuclear inspections in Iran and an Arak reactor shutdown.
The United States has only limited flexibility during the talks, however, because of scepticism in the U.S. Congress about the benefits of cutting any deal with Tehran.
U.S. Senate Majority Leader Harry Reid said on Thursday he was committed to pursuing a tougher Iran sanctions bill when the Senate returns from a recess early next month - even though President Barack Obama has warned that could derail diplomacy in Geneva.
If a preliminary agreement is reached for a six-month suspension of some of Iran's most sensitive nuclear activity, the six powers and Tehran will use that time to hammer out a broader and longer-term accord. (Additional reporting by Justyna Pawlak, Fredrik Dahl and John Irish in Geneva, Marcus George in Dubai, Steve Gutterman in Moscow, Allyn Fisher in Jerusalem, Hortense de Roffignac in Paris, Arshad Mohammed and Lesley Wroughton in Washington; Editing by Mark Heinrich, Giles Elgood and Jackie Frank)