EU foreign policy chief Catherine Ashton, center, next to members of her delegation attends talks over Iran's nuclear program in Geneva on Friday Nov. 22, 2013. AP PhotoFabrice Coffrini,Pool Iranian Foreign Minister Mohammad Javad Zarif, center, attends talks on Iran's nuclear program in Geneva on Friday Nov. 22, 2013. Iranian Foreign Minister Mohammad Javad Zarif, second right, arrives for talks over Iran's nuclear program in Geneva on Friday Nov. 22, 2013. EU foreign policy chief Catherine Ashton, second left, and Iranian Foreign Minister Mohammad Javad Zarif, third right, attend talks on Iran's nuclear program in Geneva on Friday Nov. 22, 2013. GENEVA (AP) - Secretary of State John Kerry and foreign ministers of other major powers were converging Saturday to lend their weight to the Iran nuclear talks after envoys reported progress in marathon negotiations to curb the Iranian program in return for limited sanctions relief. After a third day of talks, State Department spokesperson Jen Psaki said late Friday that Kerry was heading to Geneva to "help narrow the differences" - just hours after Russian Foreign Minister Sergey Lavrov arrived. French Foreign Minister Laurent Fabius was the first to arrive Saturday, his plane landing before dawn as the talks neared a final, pivotal stage, telling reporters: "On the Iranian nuclear issue, I want a deal - but a solid deal - and I am here to work toward that end." British Foreign Secretary William Hague announced he would also travel to Geneva. The announcements followed a day in which diplomats appeared more and more optimistic that a deal could be struck. As talks adjourned, a diplomat said Iranian Foreign Minister and top European Union diplomat Catherine Ashton had made progress on a key sticking point - Iran's claim to a right to produce nuclear fuel through uranium enrichment. Iran's official IRNA news agency quoted Iranian Deputy Foreign Minister Abbas Araghchi in Geneva as saying that Iran's right to uranium enrichment must be part of any deal. Enrichment is a hot-button issue because it can be used both to make reactor fuel and to arm nuclear missiles. Iran argues it is enriching only for power, and scientific and medical purposes. Iran has insisted on that right throughout almost a decade of mostly fruitless nuclear negotiations. But Zarif last weekend indicated that Iran is ready to sign a deal that does not expressly state that claim, raising hopes that a deal could be sealed at the current Geneva round. For the U.S. and Iran, the talks represent more than trying to hammer out a nuclear deal. In style and substance they are an extension of the historic dialogue opened during September's annual U.N. gathering, which included a 15-minute phone conversation between President Barack Obama and Iran's new president, Hassan Rouhani. The nuclear negotiations have included intensive one-on-one sessions between U.S. and Iranian envoys, offering opportunities to widen contacts and begin the long process of reconciliation after more than three decades of estrangement. For Iran, it also gives Rouhani's government a chance to show skeptical hard-liners that dialogue is possible with Washington without putting the country's Islamic system in peril. Iranian hard-liners are suspicious of talk of nuclear compromise since Rouhani took office in September, fearing his team will give too much at the negotiating table and not get enough in terms of sanctions relief. On Wednesday, Iran's supreme leader, Ayatollah Ali Khamenei, said his country would never compromise on "red lines." Since then Tehran has publicly reverted to its original stance - that the six powers must recognize uranium enrichment as Iran's right, despite strong opposition by Israel and within the U.S. Congress. Still, comments from Iranian officials in Geneva indicated that reverting to tough talk on enrichment may be at least partially meant for home consumption. In Geneva, a senior Iranian negotiator said the Iranian claim to the right to enrich did not need to be explicitly recognized in any initial deal, despite Khamenei's comment, adding that the supreme leader was not planning to intervene in the talks. He did suggest, however, that language on that point remained difficult and that there were other differences. Work is proceeding on a compromise along the lines of what the Iranian negotiator said - avoiding a direct reference to any country's right to enrich but still giving enough leeway for Iran to accept it, said a diplomat involved in the talks. Both he and the Iranian envoy demanded anonymity because they were not allowed to discuss the confidential talks and neither offered details. Senior Iranian analyst Trita Parsi, citing conversations with Iranian and U.S. officials, said the draft includes a reference to the nuclear Non-Proliferation Treaty, which Iran claims is the guarantor of each country's right to enrich by granting signatories the right to pursue nuclear power for peaceful uses. That argument is rejected by the United States and its allies, which say the treaty does not directly mention such a right. Parsi said Tehran wants the wording to make clear that Iran is not a "permanent outcast," but has the same rights and responsibilities as all other signatories to the treaty. Russia and China in recent years have signaled acceptance of Iran's demand that its right to enrich for peaceful purposes be recognized, and Germany supports the right of any country to that activity as long as it is peaceful. But the other three nations at the table with Iran - the United States, Britain and France - have continued to balk. The last round of talks between Iran and the six world powers ended Nov. 10 with no deal, even after Kerry, Lavrov, the foreign ministers of Britain, France and Germany and a Chinese deputy foreign minister flew in and attempted to bridge differences. The United States and its negotiating partners have signaled they are ready to ease some sanctions in return for a first-step deal that starts to put limits on Iran's nuclear program. They want Iran to stop enriching to a level higher than its main stockpile and only a technical step away from weapons-grade uranium as part of such a deal. They also seek limits on overall enrichment, and a formulation that reduces the proliferation danger from a reactor Iran is building that will produce enough plutonium for up to two weapons once completed. No details on relief offered have been made public. And the U.S. administration has not commented on reports from congressional officials that Obama's team estimates Iran could get $6 billion to $10 billion in benefits over six months for rolling back its nuclear program. Associated Press writers John Heilprin in Geneva, Deb Riechmann in Washington and Robert H. Reid in Berlin contributed to this report.