WASHINGTON (Reuters) - The United States said on Thursday it was still talking to Russia about extending a decades-old agreement on dismantling nuclear and chemical weapons when it expires next year, saying the two sides were discussing possible revisions.

Russian Deputy Foreign Minister Sergei Ryabkov said on Wednesday that Moscow intended to end the 1992 agreement, the latest sign that the much-vaunted "reset" in relations between the Cold War-era foes is running out of steam.

"The agreement doesn't satisfy us, especially considering new realities," Russia's Interfax news agency quoted him as saying.

But State Department spokeswoman Victoria Nuland said Washington and Moscow were still taking about the pact, known as the Nunn-Lugar Cooperative Threat Reduction program, which expires in June 2013.

"In an anticipation of that we began talking to the Russian side back in July of this year about updating that agreement, and we are continuing to have those conversations," Nuland told a news briefing.

"They have told us that they want revisions to the previous agreement. We are prepared to work with them on those revisions," Nuland said. "We want to keep talking about it and we want to solve it."

Russia's Foreign Ministry, in a separate statement issued after Ryabkov's reported remarks, suggested that cooperation could continue but under different rules.

"We have received a proposal from the American side to again extend the 1992 Agreement, which expires in June 2013. Our American partners know that this proposal does not correspond with our view of the form in which and basis upon which it would be proper to build further cooperation. For this, a more modern legal frameworks is needed, among other things," the statement said, without giving further details.

"RESET" UNDER STRAIN

Bilateral agreements including the latest START nuclear arms treaty, put in force in February 2011, have built the foundation for the U.S.-Russia "restart" initiated by Washington when Obama took office in 2008.

That treaty lowers the ceilings on stocks of long-range weapons.

But recently ties have been strained, most notably by Moscow's decision to close the office of the U.S. Agency for International Development in Moscow, which critics say is part of a broader Kremlin crackdown on pro-democracy groups.

Washington and Moscow have also been at loggerheads over the crisis in Syria, with Russia joining China in repeatedly blocking U.S.-led moves at the U.N. Security Council which sought to increase pressure on Syrian President Bashar al-Assad over his violent crackdown on armed rebels.

Outgoing U.S. Senator Richard Lugar, a veteran disarmament campaigner, was in Moscow in August to push for the renewal of the program which he helped to launch.

The project has been extended twice, most recently in 2006. U.S. officials say it has helped to deactivate more than 7,650 strategic warheads, neutralized an unspecified number of chemical weapons, safeguarded fissile materials and mitigated biological threats.

"This is a program that has paid dividends for the Russian people, for the American people. It's paid dividends globally, and we hope to be able to continue it," Nuland said.

Ryabkov said that Russia now had the finances to carry out its own programs and that Moscow was interested in continuing partnerships in third countries.

The Russian Foreign Ministry statement, while praising Nunn-Lugar, noted that Russia has been spending more of its own money on its disarmament programs, including chemical weapons destruction and the dismantling of atomic-powered submarines.

(Reporting By Andrew Quinn; additional reporting by Matt Spetalnick and Steve Gutterman in Moscow; Editing by Cynthia Osterman)