During the day's only scheduled session, Iran signaled if world powers acknowledge the Islamic republic has a right to enrich uranium under international treaties, Tehran may be willing to stop enriching uranium to 20 percent purity, considered just short of bomb-grade, The New York Times reported.
The head of Iran's parliamentary National Security and Foreign Policy Committee, Alaeddin Borujerdi, told the government-backed Mehr news agency Tuesday recognition of Iran's right to enrich is "a red line" issue that Tehran will not cede.
Western officials fear Iran's nuclear program is for development of nuclear weapons while Tehran says the program has a civilian purpose.
An Iranian diplomat with the delegation in Moscow said the outcome of the talks depends on how the world powers respond to Tehran's demands, the Times said.
Iran also seeks to ease the tough sanctions by the European Union and the United States scheduled to go in effect July 1 that would further isolate Iran from international oil and banking markets.
The Moscow talks are the third meeting between Iran and representatives from United States, Russia, China, France, Britain and Germany, following discussions in Istanbul, Turkey, and Baghdad.
A spokesman for Catherine Ashton, the European Union's head foreign policy official and lead negotiator in the talks with Iran, Monday described the first day's discussions as "intense and tough."
"They responded to our package of proposals from Baghdad, but in doing so, brought up lots of questions and well-known positions, including past grievances," spokesman Michael Mann said.
Mann said the six powers weren't offering to delay or waive any sanction until Iran demonstrated a willingness to comply with international agreements.
"Sanctions policy by definition is always under review, but can only be eased in response to real changes on the ground, so there is no question that our sanctions will come into force on the first of July," he said.