"We welcome this decision, this is a positive step," Nikolai Shingaryev, the top spokesman for the Russian Atomic Energy Ministry, told AFP.
"Russia has come under certain pressure because of Bushehr...this agreement will certainly simplify and make our cooperation easier," he added, referring to the nuclear power plant which Russia is building for Iran.
On Tuesday, Iran promised the visiting foreign ministers of Britain, France and Germany that it would show "full transparency" to the UN's nuclear watchdog and allow an intrusive inspections regime as well as halt uranium enrichment.
The deal was struck just 10 days before the end of October deadline for Iran to come clean about its nuclear programme.
Russia is building Iran's first nuclear plant, Bushehr, in a deal worth about 800 million dollars, that has provoked tensions with Washington because of US concerns that Tehran is using Russian technology to develop nuclear weapons.
Russian Foreign Minister Igor Ivanov earlier responded more cautiously to Iran's acceptance of international demands, saying that Moscow was still awaiting official notification from the International Atomic Energy Agency (IAEA).
"All this would remove the international community's concerns about Iran's nuclear programme," Ivanov said in a statement.
Top Russian officials who have negotiated with the Iranians for years say that they are never sure of a deal until the ink is dry.
The atomic energy ministry spokesman said he could not confirm Iranian officials' announcement that a separate agreement on the return of Russian spent fuel was ready for signature.
"I have no information that they're about to sign. I know that experts are conducting negotiations" but even under the best case scenario "fuel deliveries to Bushehr will not begin for a month or two," he said.
A top Iranian official said Tuesday that Tehran would sign a deal with Moscow soon promising to return supplies of Russian nuclear fuel used in the plant in southern Iran, opening the way to completion of the project.
Moscow officials have earlier claimed that negotiations over the Bushehr plant have broken down over Iran's demand for Russia to buy back the spent fuel -- a highly unusual request since spent fuel in such deals is almost always sent back for free.
Earlier this month Russia said it would push back by one year the launch of Bushehr to 2005, while denying suggestions the delay was forced by pressure from the United States or Israel.
The Vremya Novostei daily said the Iranian concessions were a relief for Moscow.
"The diplomatic success in Tehran will allow Russia to catch its breath and continue with the construction of the power station in Bushehr," said the newspaper.
But it also noted that Germany, France and Britain had reportedly promised to supply nuclear technology and fuel to Iran in return, "hardly reassuring for Russia which at this time of tension has enjoyed a quasi-monopoly in the Iranian nuclear market."