The two sides held talks Friday in the Russian capital on Iran's Bushehr power plant project, but were unable to agree on a date to sign the controversial agreement, a ministry official told the ITAR-TASS news agency.
"Talks on this point will continue in the nearest future," the official said.
The sticking point in the negotiations is the issue of return of spent nuclear fuel from the plant to Russia.
On Saturday, Moscow said it would not begin delivering fuel for the reactor until an agreement is signed on the return of spent fuel back to Russia.
"The signing of the agreement on the return of nuclear fuel... is a prerequisite for the start of deliveries of 'fresh' fuel," the atomic energy ministry source told ITAR-TASS.
Originally Russia and Iran had planned to sign an agreement under which Moscow would provide fuel for the Bushehr nuclear power plant that it has been helping build in southern Iran.
In return, Tehran was to agree to return all of the reactor's spent fuel to Russia for reprocessing.
Many Western countries, notably United States and Israel, fear that the Bushehr project could help Iran develop a nuclear weapons program and had pressed Russia not to sign the agreement until Iran allows open inspections by teams from the United Nations of its military installations.
In an apparent concession to these concerns, Russia announced the delay in the Bushehr agreement last week.
Russia's atomic energy spokesman Alexander Agapov told the Interfax news agency on August 29 that the new protocol with Iran may not be signed for several more months, blaming the delay on the Iranians.
"The delivery of fuel is constantly being delayed because Iran has no final document on a reaction to a possible emergency" during the transport of fuel, the Russian spokesman said.
"We cannot carry (spent nuclear fuel into Russia) until we are convinced it will be transported safely to a temporary storage facility," he added.
Iran hinted Saturday that it could agree to tougher nuclear inspections if ongoing talks on the issue with the UN's atomic energy watchdog removed "ambiguities".
"With explanations and the removal of ambiguities from the IAEA, Iran will in the near future will sign the additional protocol," Kamal Kharazi was quoted as saying by the state news agency IRNA.
The developments come before a key meeting of the International Atomic Energy Agency (IAEA), the UN's nuclear watchdog, which is due to discuss the Iranian question during its session September 8-11 in Vienna.