President Vladimir Putin said Monday that he saw a chance for an improvement in relations with the United States as a result of a letter he received from U.S. President George W. Bush.

The existence of the letter, public details of which remained sketchy, became known through Putin's statement to visiting U.S. Secretary of State Condoleezza Rice and Defense Secretary Robert Gates in the Kremlin on Monday.

"It's a serious document and we analyzed it carefully," Putin said of the letter. "If we manage to agree on its main provisions, we will be able to say that our dialogue is progressing successfully."

Putin said that, while there was hope that some bilateral issues were closer to resolution, there was much that still needed to be sorted out. He added that he and Bush had discussed these issues in a recent telephone conversation.

It was not clear whether the proposed U.S. missile-defense system in Central Europe, a plan that has caused severe tensions with Moscow, was the topic of the letter from Bush, and a U.S. embassy spokeswoman, speaking on customary condition of anonymity, said Monday evening that she could not immediately comment on its contents.

An unidentified Pentagon official traveling with Gates said the letter dealt with the agenda for the current visit, Reuters reported. A Kremlin source said the letter spoke of the "legacy both presidents are leaving behind," Interfax reported.

Rice and Gates came to Moscow out of turn in the customary schedule of bilateral talks in hopes of making progress on a number of thorny issues that have placed relations at or near their worst since the end of the Cold War.

Talking with Putin, Rice praised the two-on-two format for the meetings with Foreign Minister Sergei Lavrov and Defense Minister Valery Serdyukov, while thanking the president for "taking the time to be with us personally."

The visit is the first by major U.S. officials since the March 2 presidential election.

Before the discussion with Putin, Rice and Gates met with President-elect Dmitry Medvedev.

They were scheduled to hold bilateral talks with Lavrov and Serdyukov on Tuesday, in meetings that were expected to last five to six hours, Pentagon spokesman Geoff Morrell said.

A major topic of discussion was to be U.S. plans to build a radar site in Czech Republic and deploy 10 missile interceptors in Poland as part of an anti-missile shield. Russia has steadfastly described the system as a threat to its security, concerns that have not been helped by a recent proposal from Washington that a radar site also be set up in Turkey.

Two Cold War-era agreements -- The Treaty on Conventional Armed Forces in Europe, which Russia suspended last year, and the Strategic Arms Reduction Treaty, which expires next year -- will also be addressed.

Putin's guardedly positive statement Monday came in contrast to efforts by both sides ahead of the talks to dampen expectations for any significant progress on the missile-defense issue. U.S. officials stressed that they would not make any new offers, while Moscow said new overtures were necessary.

Deputy Foreign Minister Alexander Grushko said in an interview published Monday that Washington too had to make a contribution if an agreement was to be reached.

"We would prefer measures of cooperation, not confrontation," said Deputy Foreign Minister Alexander Grushko, Nezavisimaya Gazeta reported. "But this choice does not depend only on us."

A source in the Defense Ministry said progress was only likely if Rice and Gates "bring with them new proposals that take into account Moscow's concerns," Itar-Tass reported.

"Otherwise ... everything will be reduced to each side repeating positions that have been known for a long time," the source said.

But the Pentagon's Morrell reiterated on the sidelines of Monday's meeting that nothing new was on the table.

"We come armed with no new proposals," he said, adding that the purpose of this visit was to demonstrate that the United States planned to "stand by its proposals. We are not going to sweeten them."

He added that Rice and Gates were looking to "flesh out the proposals that were made in October," referring to a visit to Moscow during which Putin criticized Washington's resolve in pushing forward with missile-defense plans.

The current visit has been seen by some as an attempt by Bush to soothe Moscow's worries ahead of the NATO summit in Bucharest in early April. Putin and Bush are to meet on the sidelines of the summit, in what will likely be their last meeting in office.

The meeting with Medvedev took place in a lighter atmosphere, with the president-elect telling Rice, "We have the will and determination to move forward," in nationally televised comments.

Rice, for her part, congratulated Medvedev on his election victory, adding, "We have had good relations with you for a long time and hope they will remain good."

Gates, wearing a sling after breaking his arm in a fall, joked that the injury could get in his way during the talks.

"With a broken arm, I won't be nearly as difficult a negotiator," Gates told Medvedev, who responded in Russian, "We'll see."