Bush is accepting Putin's invitation for a meeting in the Black Sea resort city of Sochi on April 6, to come at the end of the president's trip that starts Monday to Ukraine, the NATO summit in Bucharest, Romania, and Croatia. It will likely be the last meeting between Bush and the Russian leader before Putin leaves office.
Putin's successor as Russian president, Dmitry Medvedev, takes office at the beginning of May.
Bush said he and Putin would discuss the missile defense system that the United States plans to base in Central Europe. It would involve 10 interceptor missiles based in Poland and a tracking radar system in the Czech Republic.
Moscow has been vehemently opposed to the idea, saying the intent is to weaken its nuclear deterrent. The United States denies that, saying the facilities are being designed to protect Europe against a potential missile attack - or even just nuclear blackmail - by Iran.
The dispute has become heated, with increasingly confrontational rhetoric coming from Moscow. But there have been signs of cooling recently and Bush told reporters that he saw an opportunity to build on that.
Talks in Moscow between high-level Russian officials and Secretary of State Condoleezza Rice and Defense Secretary Robert Gates yielded some progress, said Stephen Hadley, Bush's national security adviser. Since those talks, Russia has made some conciliatory statements.
A Russian delegation is in Washington this week for more discussions "and continues to have some progress," Hadley said.
He said the U.S. is trying hard to come up with "a formula of measures" that will ease Russia's concerns, perhaps by making Moscow an equal partner in the system and increasing transparency.
But the meeting also could be viewed as an effort to firm up a crucial, though faltering, relationship for the United States before the two leaders who have worked together so long both leave office.
Though Putin has said he will switch roles to become prime minister, there are concerns in Washington about the direction Russian foreign policy might take under Medvedev at a time when Russia is a key factor in dicey issues such as containing nuclear programs in Iran and North Korea.
"This is an opportunity for the two leaders to meet, assess what progress has been made and see whether we can come together with a framework that can, as I said, consolidate areas where we're cooperating together, maybe resolve some outstanding issues such as missile defense and provide a platform for the relationship between the two countries going forward," Hadley said.
Other issues on the table, he said, include whether to extend the Moscow Treaty of 2002 with a new verification regime for strategic nuclear arms reductions and a replacement for the 1991 START accord that expires next year.
Bush declined to comment on what he thinks democracy will be like in Russia under Medvedev, Putin's protege and hand-picked successor. U.S. concerns about democratic backsliding in Russia were already on the rise before the Kremlin's power was enlisted to help smooth Medvedev's election.
Bush first said he had not yet met Medvedev, though the White House has said the two met once four years ago when the Russian was a government minister. Bush quickly then said "I have yet to work with him."
He said he liked some things he's heard Medvedev say, but he said he would be "listening very carefully" as time goes on and suggested he would withhold judgment on the new president's leadership until after he has dealt with him.
