By Jill Dougherty, CNN Foreign Affairs Correspondent

The State Department maintained Thursday that a long-standing partnership with Russia to dismantle and safeguard weapons of mass destruction from the Soviet Union's once-massive arsenal is not dead, as Russian media has reported.

Russian officials, however, indicated they had no intention of extending the agreement - at least in its present form - dealing a serious blow to cooperation between the two countries.

The Nunn-Lugar Cooperative Threat Reduction program, which has spent approximately $7 billion in its two decades, financed primarily by the U.S. government, has deactivated more than 7,500 nuclear warheads, implemented security upgrades at Russian's nuclear storage sites, neutralized chemical weapons, safeguarded fissile materials, converted weapons facilities for peaceful use, and mitigated biological threats.

"We are still in talks," State Department spokeswoman Victoria Nuland told reporters in Washington Thursday. Russia officials "have told us that they want revisions to the previous agreement. We are prepared to work with them on those revisions, and we want to have conversations about it."

But in Moscow, the Russian Foreign Ministry issued a statement saying, "Our American partners know that their proposal is at odds with our ideas about the forms and basis for building further cooperation in that area."

While Moscow "has a positive view" on the program's cooperation, the ministry said, "a more modern legal framework" is needed."

The current agreement on Nunn-Lugar cooperation expires in June of 2013 and U.S. officials have been talking with their Russian counterparts since July about updating the agreement, Nuland said.

"We as a government greatly value the ongoing Nunn-Lugar Cooperative Threat Reduction Program," Nuland said. "We believe there is a lot of future work for the U.S. and Russia to do together in the CTR space, including cooperation that we do in this area with third countries ... other former Soviet states."

Former Sen. Sam Nunn, one of the co-sponsors of the Nunn-Lugar program, told CNN, "I don't think the Russians have ruled out having a new umbrella agreement that would have a different framework. This framework was put together when the Russian treasury was empty."

Nunn said that in his opinion, Moscow today is sensitive about key aspects of the program. Russia, he said, "does not want to look like they're taking aid on something that's a security issue in Russia."

Another issue for Russia, he added, is the question of access.

"Access follows money," he said, "and we've had unprecedented access to many facilities that the Russians would have never acceded to allow us to have access to if it had not been for their financial plight and the realization in Russia in the early 1990s that they had huge problems with their nuclear, chemical and biological weapons as well as materials."

The move comes at a politically sensitive time in the United States, when the Obama administration is under attack for what Republicans describe as a failed "reset" policy with Russia. In early October, the Russian government announced that it was ending U.S. Agency for International Development programs in the country.

The State Department's spokeswoman denied there was any connection between that move and the current difficulty in reaching agreement on extending Nunn-Lugar.

Russia expert Matthew Rojansky of the Carnegie Endowment for International Peace told CNN that the United States, eventually, is going to have to adjust its approach on Nunn-Lugar. "At some point, some version of this was going to happen, that's true, if for no other reason than ... we cannot fund global security forever," he said.

"Whether it was going to happen in this dramatic form, in this absolute form, that is a function of the relationship not being as good as it could be. The relationship is not working right, right now, that's for sure ... on both sides."

Nunn meanwhile, says Nunn-Lugar has paid dividends over its 20 years and he holds out hope that "something that could be much more of a partnership could emerge from this."

"With the lessons learned and the best practices we've had of two decades of working together," he told CNN, "I think that partnership could be very valuable for the U.S., for Russia and for the globe. But it will be on much more of a reciprocal access basis.

"The Russians swallowed their pride a lot in the 1990s and the last 20 years, and I think we have to recognize that reciprocity is going to be the order of the day. ... In other words, they will say trust is a two-way street."

Whether the United States will be willing to do that, Nunn added, is a question, "but it seems to me it's fundamentally in our interest and their interest."

"The fact that the United States and Russia have 90 to 95% of all the nuclear weapons and materials in the world indicates that there's got to be a partnership if this problem is going to be tackled."