In their first sit down as heads of state, Mr. Bush called Medvedev a "smart" guy who is well versed in foreign policy. Medvedev casually referred to Mr. Bush as "George." Yet they inched no closer on the missile defense issue during their more than hour-long discussion on the sidelines of a summit here.
A Kremlin aide described the private meeting as open and constructive, but said it led to no progress on the missile-defense issue.
The public comments by the two presidents only glossed over Russia's anger about the topic. And they both brushed off the fact that their official relationship will expire in fewer than 200 days when the Bush presidency ends.
"We will build on the relationship with the new American administration," said Medvedev. "But we still have six months with the effective administration and we'll try to intensify our dialogue with this administration."
The Russian leader said he and Mr. Bush agreed on curtailing the nuclear weapon capability of Iran and North Korea.
"But then certainly there are others with respect to European affairs and missile defense where we have differences," Medvedev said. "We would like to agree on these matters, as well, and we also feel very comfortable in our dealings with George."
Like former Russian President Vladimir Putin, still the top powerbroker in Moscow, Medvedev remains critical of the West, in particular the United States. He has shown no sign of softening opposition to U.S. plans for missile defense facilities in Europe or to NATO's promise to eventually invite Georgia and Ukraine in.
Personal relations between the two appear warm, but the U.S. leader didn't go as far as to repeat what he said about Putin when he first met him in June 2001. Then, Mr. Bush said he looked into Putin's eyes and "was able to get a sense of his soul."
"I'm not going to sit here and psychoanalyze the man, but I will tell you that he's very comfortable, he's confident, and that I believe that when he tells me something, he means it," Mr. Bush said.
The two, however, are at opposite ends of their political lives. Mr. Bush is on his way out and Medvedev just took office in May. This is the American President's eighth and final G-8. This is Medvedev's freshman year at the summit.
The two leaders, who also are also are united in their fight against international terrorism and want to see a Middle East peace accord and a future for Afghanistan, talked on the sidelines of the Group of Eight summit of industrialized nations. Japan is hosting the event at a heavily guarded luxury resort atop Poromoi Mountain in Hokkaido, an island in northern Japan.
From there, visitors normally can see the doughnut-shaped Lake Toya, formed in a crater of a collapsed volcano. Not Monday. Sheets of rain pelted the scenic mountain and the weather offered a metaphor for the contentious U.S.-Russia discussions on missile defense: Fogged in.
U.S. and Polish officials are negotiating to base American missiles in Poland for a future missile shield against Iran. Still, there is no guarantee the shield will ever be built or would work as advertised. Negotiations over the 10 missile interceptors are proving more contentious than the U.S. had anticipated.
The site would be linked to a missile-tracking radar system that Washington wants to place in the Czech Republic. The Czech government has agreed in principle to the plan, but parliament's approval is still needed.
Russia is staunchly against the U.S. plans, arguing that U.S. military installations in former Soviet satellites so close to its borders would pose a threat to Russian security. Moscow has threatened to aim its own missiles at any eventual base in Poland or the Czech Republic.
The U.S. maintains that the plan poses no threat to the Kremlin's vast nuclear arsenal.
After the talks, a Kremlin aide accentuated the positive in U.S.-Russian relations, but said Mr. Bush and Medvedev made no progress on the missile-defense issue - the major point of disagreement between them.
Sergei Prikhodko said the talks were "exclusively well-intentioned, constructive, and open, but at times critical."
Mr. Bush and Medvedev met on the opening day of the summit, a day focused on aid to Africa and on whether the world's economic powers were providing enough financial assistance to fight disease and improve health care.
The American President is calling on G-8 nations to write checks to make good on their pledges to help battle HIV-AIDS, malaria and other diseases. He and other G-8 heads met with leaders of seven African nations to discuss aid to the continent, but the election crisis in Zimbabwe also was high on their agenda.
Mr. Bush backs U.N. sanctions against Zimbabwe, whose president, Robert Mugabe, is accused of using violence and intimidation to win a runoff election last month. "I am extremely disappointed in the elections, which I labeled a sham," Mr. Bush said alongside Tanzanian President Jakaya Kikwete.
Many African nations, though, are reluctant to pursue sanctions. Kikwete, the current head of the African Union, said that African leaders share U.S. concerns about Zimbabwe. But he told the U.S. president, "the only area that we may differ is on the way forward."
Meanwhile, a consensus still appeared elusive on a statement on climate change, said Jim Connaughton, chairman of the White House Council on Environmental Quality. The Group of Eight takes up the divisive issue on Tuesday.
At issue is an agreement from last year's G-8 summit in Germany to seriously consider a goal of halving emissions by 2050.
But coming up with a more detailed target for cutting emissions is proving difficult. The Bush administration is unwilling to consider such a target unless developing economies that are also big polluters, like China and India, are included.
"The president has made clear that we believe a long-term goal is useful and necessary," Connaughton said Monday. "The president has also made clear that it's a goal that must be shared by all countries."