The talks are being held in Moscow, and it includes Iran and six world powers, who are back at the bargaining table over nuclear activity.
The United States, Russia, China, Britain, France and Germany want Iran to curb nuclear enrichment, which can be used to make reactor fuel and arm nuclear warheads.
Negotiations deadlocked after two recent talks. Iran says it has a right to enrich and denies accusations that it is doing so to make weapons.
Iran wants sanctions lifted or postponed, but the six powers say neither will happen until Tehran complies with their demands.
However, Monday's meeting seemed to bring no solid conclusions, as the sides are no closer to agreement than at their last session in May in Baghdad, which ended with them far apart.
The six diplomats say they hoped Iranian chief negotiator Saeed Jalili would respond directly to their demand that his country stop enriching to 20 percent. Instead, they said Jalili presented his side's conditions for negotiations, including a request to lift all sanctions.
The diplomats spoke under condition of anonymity because they were not authorized to talk about the closed session.
The Islamic Republic has mentioned lifting sanctions before, but one of the diplomats said that its request at the closed Monday meeting was the most direct to date.
Diplomats from several nations meeting with Iran in Moscow say the talks are significant. They say it could be the last in a series, and if negotiators fail to make headway in persuading Tehran to stop higher-grade uranium enrichment, it remains unclear if or when new talks would occur.
The Associated Press contributed to this report.