It was the first such high-level contact between the two sworn enemies since Iran's 1979 revolution, which sent relations between the two into a deep freeze.
Israel: Don't relax sanctions too early
Israeli Prime Minister Benjamin Netanyahu urged the international community not to relax too soon the painful economic sanctions that have put Iran's leaders under "intense pressure" to return to talks.
"I think it would be a historic mistake to ease the sanctions when they are so close to achieving their goals," he said.
"Now is an opportune moment to reach a genuine diplomatic solution that peacefully ends Iran's military nuclear program.
"This opportunity can only be realized if the international community continues to place pressure on Iran, because it is that pressure that has brought Iran back to the negotiations in the first place. And it is that pressure which makes the peaceful dismantling of Iran's military nuclear program possible."
Israel's Security Cabinet also warned Tuesday against conceding too much too soon to the Iranians.
"Israel does not oppose Iran having peaceful nuclear energy. This does not require uranium enrichment or plutonium. Iran's nukes prog does," Netanyahu spokesman Ofir Gendelman said via Twitter.
A country that "regularly deceives the international community" does not have a "right to enrich" as Iran claims, he said.
A senior Obama administration official told reporters in Geneva that the administration would be willing to consider quick relief on sanctions "targeted in proportion" to what Iran puts on the table, should it be prepared to curtail the pace and scope of its uranium enrichment program, offer steps to improve transparency of its nuclear program, and address concerns about its stockpile of enriched uranium.
Larijani: 'We are ready'
Ali Larijani, Iran's powerful parliamentary speaker and a close associate of the nation's supreme leader, Ayatollah Ali Khamenei, said last week that Iran is serious about resolving the dispute over its nuclear program.
It is keen to resolve the issue "in a short period of time," Larijani told CNN's Christiane Amanpour in an exclusive interview from Geneva. "From Iran's side, I can say that we are ready," he said.
"If the Americans and other countries say that Iran should not develop a nuclear bomb or should not move towards that, then we can clearly show and prove that. We have no such intention. So it can be resolved in a very short period of time."
Nonetheless, Larijani said, the West must accept Iran's right to enrich nuclear fuel for civilian purposes, as allowed under the Treaty on the Non-Proliferation of Nuclear Weapons, to which Iran is a signatory.
Some believe that Iran's recent apparent willingness to negotiate seriously over its nuclear program is a result of the crippling sanctions on its economy.
Shortly after this year's U.N. General Assembly ended, a U.S. State Department official said the United States would be prepared to consider relaxing certain sanctions on Iran if it took confidence-building steps to prove its sincerity to negotiate over its nuclear program.
But this will take time and the building of trust.
U.S. Under Secretary of State Wendy Sherman, who is in Geneva, stressed that the entire sanctions regime targeting Iran would not be lifted "any time soon" unless the array of concerns about Iran's nuclear program was fully addressed.