Lavrov arrived in Geneva as diplomats were struggling to find language acceptable to Iran and its six negotiating partners.
Iran's claim to a right to produce nuclear fuel apparently is a key sticking point. Iranian Foreign Minister Mohammad Javad Zarif and Catherine Ashton, the European Union's top diplomat, have met repeatedly since Wednesday trying to resolve that and other differences.
The last round of talks between Iran and the six world powers ended on November 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.
Ashton is convening the negotiations, and protocol dictates that foreign ministers come only at her invitation. Ashton's spokesman Michael Mann said she did not issue any invitations this time. That suggested that a deal was not yet in the cards and that Lavrov was in Geneva at his own initiative.
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Iran says it is enriching only for reactor fuel, medical uses and research. But the technology can also produce nuclear warhead material.
Zarif last weekend indicated that Iran is ready to sign a deal that does not expressly state Iran's right to enrich, raising hopes that a deal could be sealed at the current Geneva round.
On Wednesday, however, Iran's supreme leader, Ayatollah Ali Khamenei, said his country would never compromise on "red lines." Since then Tehran has reverted to its original line - that the six powers must recognise this activity as Iran's right under the nuclear Nonproliferation Treaty despite strong opposition by Israel and within the US Congress.