Russian President Vladimir Putin on Friday warned that U.S.-Russia relations could be at stake if the United States pursues missile defense systems in Eastern Europe.

Secretary of State Condoleezza Rice and Defense Secretary Robert Gates arrived at the president’s country house outside Moscow at 10:30 a.m. for the meeting with Putin, who showed up 40 minutes later.

"Of course, we can sometime in the future decide that some anti-missile defense system should be established somewhere on the moon,” Putin said, “but before we reach such arrangements, we will lose the opportunity of fixing some particular arrangements between us."

The Russian leader also threatened to pull his country out a Cold War-era treaty limiting intermediate-range missiles unless other countries sign on to the agreement.

"If we are unable to attain such a goal" Putin said, "it will be difficult for us to keep within the framework of the treaty in a situation when other countries do develop such weapons systems, and among those are countries in our near vicinity."

Gates said Washington was interested in limiting missile proliferation in Iran.

The Russian government sees the U.S. missile defense plan, which Washington describes as a hedge against the threat of missile attack from Iran, as a worrisome step toward weakening Russian security. It has been a longstanding dispute, and Putin's remarks seemed to raise the level of tensions.

"We have an ambitious agenda of security issues that concern both of us, including, as you suggest, development of missile systems by others in the neighborhood, I would say in particular Iran," Gates said.

"Even though we have our differences, we have a great deal in common because that which unites us in trying to deal with the threats of terrorism, of proliferation, are much greater than the issues that divide us," Rice said.

Russian Foreign Minister Sergey Lavrov said at the start of the meeting that the Americans had presented "detailed proposals" to Putin on missile defense and arms control and a treaty on reducing conventional forces in Europe.

He offered no details but said the Russian government is ready to seek compromise, noting in particular Putin's eagerness to expand the treaty on intermediate missiles.

But both he and Rice said the two countries were committed to bridging those gaps.

"I know that we don't always see eye-to-eye on every element of the solutions to these issues," Rice said. "Nonetheless, I believe we will do this in a constructive spirit, that we will make progress during these talks as we continue to pursue cooperation."

"We will try to find ways to cooperate," Rice responded, looking at notes she had jotted while frowning at Putin as he spoke from what appeared to be a prepared text.

Referring to the Intermediate-range Nuclear Forces treaty negotiated between the United States and the former Soviet Union, Putin said it must be applied to other countries, including those "located in our near vicinity." He did not mention any by name, but in response, Gates said Washington was interested in limiting missile proliferation in Iran.

Putin said the treaty must be made "universal in nature."

The pact eliminated the deployment of Soviet and American ballistic missiles of intermediate range and was a landmark step in arms control just two years before the fall of the Berlin Wall and later the breakup of the Soviet Union.

"We need to convince other (countries) to assume the same level of obligation as assumed by the Russian Federation and the United States," Putin said. "If we are unable to obtain such a goal ... it will be difficult for us to keep within the framework of the treaty in a situation where other countries do develop such weapon systems, and among those are countries located in our near vicinity."

Gates said the Pentagon was ready to intensify a dialogue on the matter.

"We have an ambitious agenda of security issues that concern both of us, including, as you suggest, development of missile systems by others in the neighborhood — I would say in particular, Iran," he said.

Gates did not directly comment on the missile defense dispute.

Putin also has threatened to suspend Russian adherence to another arms control treaty, known as the Conventional Forces in Europe pact, which limits deployments of conventional military forces. Moscow wants it to be revised in ways that thus far have been unacceptable to U.S. and European signatories.

On missile defense, Putin was particularly pointed in his remarks, in which sought to lay out his view of what Rice and Gates should be discussing with Lavrov and Russian Defense Minister Anatoly Serdyukov.

"We hope that in the process of such complex and multi-faceted talks you will not be forcing forward your relations with the eastern European countries," the president said. He then made his remark about the possibility of one day putting a missile defense system on the moon.

Shortly before the talks with Putin, Lavrov had strolled into the house's billiards room, where American reporters had gathered, for a cigarette break. He was asked whether he expected any breakthroughs in the talks and offered a perhaps prophetic quip.

"Breaks, definitely. Through or down, I don't know," he said.

The Pentagon plans to install 10 missile interceptors in Poland, linked to a missile tracking radar in the Czech Republic. The Pentagon says the system will provide some protection in Europe and beyond for long-range missiles launched from Iran, but Russia believes the system is a step toward undermining the deterrent value of its nuclear arsenal.

Rice told reporters on Thursday on her flight to Moscow that the U.S. would go ahead with the program as planned.

"We've been very clear that we need the Czech and Polish sites," she said, although there's "considerable interest" in Russian ideas for cooperation such as sharing a Soviet-era tracking station in Azerbaijan.

FOX News’ Jennifer Griffin and The Associated Press contributed to this report.