But Israeli Prime Minister Benjamin Netanyahu insisted any agreement in the making was a "bad deal" that gave Iran a pass by offering to lift sanctions for cosmetic concessions that Netanyahu said left intact Tehran's nuclear weapons-making ability.
Asked about Netanyahu's criticism, White House spokesman Josh Earnest said "any critique of the deal is premature" because an agreement has not been reached.
The White House later said President Barack Obama called Netanyahu to update him on the ongoing talks and said Obama affirmed he's still committed to preventing Iran from obtaining a nuclear weapon. The White House said Obama and Netanyahu will stay in close contact.
Kerry tempered reports of progress, warning of "important gaps" that must be overcome in the elusive deal that would offer limited sanctions relief if Iran starts capping programs that could make atomic weapons.
Lavrov also was joining the talks, Russia's RIA Novosti news agency reported. His deputy, Sergei Ryabov, was quoted as saying that Moscow expects them to produce a "lasting result expected by the international community."
A Western diplomat in Geneva told The Associated Press that China is sending a deputy foreign minister to the talks. The diplomat spoke on condition of anonymity because he was not authorized to provide such information.
"The negotiations have reached its critical, very sensitive situation, and it needs decisions at higher levels," Araghchi said in comments broadcast on Iranian PressTV.
Any agreement would be a breakthrough after nearly a decade of mostly inconclusive talks, but would only be the start of a long process to reduce Iran's potential ability to produce nuclear arms, with no guarantee of ultimate success.
Kerry arrived from Tel Aviv after meeting Netanyahu and trying to defuse concerns. Israel is strongly critical of any deal that even slightly lifts sanctions unless Iran is totally stripped of technology that can make nuclear arms.
The talks primarily focus on the size and output of Iran's enrichment program, which can create both reactor fuel and weapons-grade material suitable for a nuclear bomb. Iran insists it is pursuing only nuclear energy, medical treatments and research, but the U.S. and its allies fear that Iran could turn this material into the fissile core of nuclear warheads.
Kerry said there were "some very important issues on the table that are unresolved."
He met later Friday with his European counterparts before joint talks with Zarif and Catherine Ashton, the European Union's top diplomat who is convening the talks.
In earlier comments to Israeli television, Kerry suggested Washington was looking for an Iranian commitment to stop any expansion of nuclear activities that could be used to make weapons, as a first step.
"We are asking them to step up and provide a complete freeze over where they are today," Kerry said Thursday.
Six powers the negotiators also include Russia and China are considering a gradual rollback of sanctions that have crippled Iran's economy. In exchange, they demand initial curbs on Iran's nuclear program, including a cap on enrichment to a level that can be turned quickly to weapons use.
Iran, which denies any interest in such weapons, currently runs more than 10,000 centrifuges that have created tons of fuel-grade material that can be further enriched to arm nuclear warheads. It also has nearly 440 pounds (200 kilograms) of higher-enriched uranium in a form that can be turned into weapons much more quickly. Experts say 550 pounds (250 kilograms) of 20 percent-enriched uranium are needed to produce a single warhead.
The six have discussed ending a freeze on up to $50 billion (37 billion euros) in overseas accounts and lifting restrictions on petrochemicals, gold and other precious metals. But their proposal would maintain core sanctions on Iran's oil exports and financial sector, as an incentive for Iran to work toward a comprehensive and permanent nuclear accord.
A semiofficial Iranian news agency quoted a member of Iran's negotiating team as saying that Iran has asked for the lifting of oil and banking sanctions.
"We have announced to the Western side that the issue of oil and banking sanctions has to be taken into consideration in the first step," Majid Takht-e Ravanchi was quoted as telling a Mehr reporter in Geneva.
"We can't judge at this point whether we will reach a deal or not," he said.
While Tehran could be pressing for more significant sanctions relief, comments from Lavrov suggested an even more basic disagreement Iran's insistence that the six recognize what it calls its "right" to enrich uranium.
Washington and its Western allies say such a right does not exist, despite Tehran's claim that it is enshrined in the nuclear Nonproliferation Treaty. Lavrov, in comments to reporters in Moscow, said Russia believes a deal should recognize Iran's right to enrich, adding once that happens, "it will be possible to start moving forward."
Israel has been watching the talks with deep concern. It has frequently dangled the prospect of military action against Iran should negotiations fail to reach the deal it seeks a total shutdown of uranium enrichment and other nuclear programs Tehran says are peaceful but which could technically be turned toward weapons.
"I understand the Iranians are walking around very satisfied in Geneva, as well they should because they got everything and paid nothing," Netanyahu told reporters before meeting Kerry.
Members of Congress were awaiting the details of any deal between Iran and world powers, but hard-liners were pushing for even stricter sanctions that go well beyond the ones crippling Iran and that the Islamic Republic is hoping to ease. Despite the talks in Geneva, proposed new sanctions could show up as amendments to a defense authorization bill that the Senate will debate later this month.
Rep. Ed Royce, the Republican chairman of the House Foreign Affairs Committee, announced he will convene a hearing Wednesday to examine the negotiations with Iran. He said the negotiations carry the risk of "seriously weakening" sanctions, which would be hard to tighten if the Iranians don't abide by the deal.
Many of the lawmakers have the same demand as Netanyahu: They want enrichment to stop altogether in exchange for loosening sanctions.
"Any agreement that does not require the full and complete halting of the Iranian nuclear program is worse than no deal at all," said House Majority leader Eric Cantor. "We should not race to accept a bad deal, but should keep up the pressure until the Iranians are willing to make significant concessions."
Iran's new moderate leadership is being pushed by hard-liners seeking significant sanctions reductions in exchange for scaling back enrichment.
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AP Diplomatic Writer Matthew Lee, AP writers Donna Cassata in Washington and Vladimir Isachenkov in Moscow, and AP White House Correspondent Julie Pace contributed to this story.
