Bush and Putin have recently disagreed over the anti-missile system that Washington plans to build in Poland and the Czech Republic and which Russia sees as a military and strategic threat.
Putin has suggested the US could share a Russian-controlled radar as part of the system, instead of basing all of it in central Europe.
They have also taken opposing positions on independence for the breakaway Serbian province of Kosovo and Bush has accused Putin of opposing democratic reforms.
The US president is also expected to seek support from the Kremlin for tough new penalties against Iran over its suspected nuclear weapons programme.
A few hours before the Russian leader arrived on Sunday, more than 1,000 protesters rallied nearby against the ongoing war in Iraq and other areas of US foreign policy.
Although Putin has been among the most outspoken critics of Bush's Iraq policy, the war is not expected to figure prominently in talks during his visit, which will last less than 24 hours.
|Anti-war critics gathered near the Bush family |
home ahead of Putin's arrival [AFP]
The visit began on Sunday with wide smiles, warm handshakes, a lobster dinner and a fast boat ride in the Atlantic ocean.
George Bush Sr, Bush's father and former president, received Putin at a nearby airport on Sunday, accompanying him by helicopter and limousine to the compound.
Putin brought large bouquets of flowers for first lady Laura and former first lady Barbara.
The elder Bush then piled his son and the Russian leader into his speedboat, Fidelity III, for a fast ocean ride, before settling down to dinner.
After the meeting Putin will continue to Guatemala where Olympic officials are picking a host city for the 2014 winter games.
The Black Sea resort of Sochi is one of the candidate cities.
Source: Al Jazeera and agencies