Bush flew to Russia after a stopover in Croatia, which along with Albania was invited to join NATO at the three-day summit which concluded in Bucharest Friday.
The U.S. leader and President Vladimir Putin are expected to meet for an informal dinner today, and will begin negotiations on Sunday. Bush will also meet Sunday with Russian president-elect Dmitry Medvedev, who is set to take over in the Kremlin on May 7 when Putin steps down.
At the NATO summit, the bloc's members rejected Bush's calls for membership talks to be started with Georgia and Ukraine. Macedonia's membership plans were postponed by Greece's veto.
The talks between the Russian and U.S. leaders, a continuation of their meeting at the NATO summit which Putin attended as a guest, is again likely to focus on missile defense and NATO expansion. The agenda will also include a broader strategic security deal between the two countries.
After meeting with NATO leaders on Friday, Putin said that any further NATO expansion toward Russia's borders would be interpreted as a direct security threat, but ruled out a new Cold War.
"The appearance on our borders of a powerful military bloc... will be considered by Russia as a direct threat to our country's security," he said.
In a bid to make up for his recent confrontational rhetoric, Putin highlighted some positive aspects of cooperation with the Western bloc, including Russia's consent at Friday's talks to transit NATO non-military supplies to the alliance's troops engaged in anti-terrorism operations in Afghanistan.
Putin said Friday's discussions had been "constructive," and called for closer ties with NATO to tackle differences that include an amended Cold War-era Conventional Forces in Europe (CFE) treaty and Washington's missile defense plans for Europe. The issues have plunged Russia's relations with the West to a post-Cold War low.
Putin also said Friday he was happy that Russia's concerns over U.S. plans to deploy a missile base in Poland and a radar in the Czech Republic had been heard by NATO, and that Washington and Moscow would continue to discuss the issue.