An official said Western negotiators were ready to take appropriate steps in exchange for "verifiable Iranian actions" regarding its nuclear program, The New York Times reported.
After a meeting in Baghdad in May, "the common ground was fairly narrow," the Western official said.
"We all have to remember what we are doing here," the official said. "The international community's concern is to stop Iran from acquiring a nuclear weapon. That is what it is fundamentally about."
New sanctions on Iranian oil exports and bank transactions are to go into effect by July 1.
The Moscow talks between Iran and major world powers continued stalled negotiations that began years ago but recently resumed in Istanbul, Turkey, and Baghdad.
Iran is in violation of U.N. Security Council resolutions demanding that it suspend uranium enrichment and hasn't assured the international community its nuclear program is for peaceful purposes, not developing nuclear weapons capability as Western leaders fear.
Negotiators representing the United States, Russia, China, France, Britain Germany and the European Union were expected to renew demands that Iran suspend the enrichment of uranium to 20 percent, move its stockpile of this uranium and stop operations at an enrichment facility inside a mountain near Qom.
A proposal raised in Baghdad offered Iran parts for older U.S.-built civilian aircraft and safety upgrades for an Iranian nuclear reactor if Tehran suspends the enrichment program, the Times said. Western negotiators also were expected to raise the promise of more relief from sanctions relief for specific actions to come into compliance.
Tehran is seeking more substantial concessions, such as complete sanctions relief and recognition of its right to enrich uranium.
A spokesman for the European Union negotiating team said Monday he hoped Tehran would "seriously engage" on previously offered proposals, the Times said.
"In terms of any adjustments … what is on the table is what was put on the table in Baghdad," said Michael Mann, spokesman for the European Union's top foreign policy official, Catherine Ashton. "It's in black and white on paper, and it's there for all to see, so we're hoping they can take it point by point."
An Iranian negotiator said Monday the Moscow talks were unlikely to produce an agreement, RIA Novosti reported.
"As of right now the chances of making progress in Moscow are very small, minimal," head Iranian negotiator Saeed Jalili said. "We have our principles. If the Group of Six accepts our proposals we will be ready to accept theirs."