Both leaders on Thursday entered discussions cautiously, wanting to air their grievances without undercutting generally improved relations between the old Cold War nuclear rivals who are cooperating in the "war on terror".
The leaders opened talks in the Slovakian capital Bratislava at a medieval castle overlooking the snow covered city and the Danube River, aides inked an agreement designed to counter nuclear terrorism, in part by restricting the availability of shoulder-fired missiles capable of bringing down aircraft.
Bush prefaced his meeting with the Russian leader - their first since Bush's new term began in January - with a speech in a crowded town square hailing the spread of democracy to former Soviet republics like Slovakia.
High on the meeting agenda are US concerns over Putin's moves to solidify his power and clamp down on civil and press liberties. Also drawing US alarm are Putin's attempts to influence elections in Ukraine, Russian arms sales to Syria and the Kremlin's close ties to Iran.
But Bush seeks to balance those concerns with a desire for continued cooperation on security issues such as terrorism, weapons proliferation and energy.
Putin's clamp down on liberties
are high on the meeting's agenda
For their part, Russian officials dislike what they see as US meddling in their internal affairs and in former Soviet republics where Moscow's influence is waning as some new leaders look westward. Putin argues that the Russian people are accustomed to strong rule by czars and a large government role in everyday life.
Putin has sent mixed signals - offering conciliatory talk aimed at boosting Russia's international standing and its chances for membership in the World Trade Organisation, but at other times saying America has double standards on terrorism and is seeking to spread a dubious form of democracy.
The two leaders arrived to a red carpet ceremony in the courtyard of the red-roofed Bratislava Castle, exchanging handshakes and smiles. About a dozen troops, clad in fur-trimmed red and blue uniforms, stood at attention.
Elsewhere in the capital, security was tight. Hundreds of heavily armed police officers and sharpshooters kept watch and helicopters flew overhead.
Under the new agreement, both nations would share information, take inventories of such weapons, destroy "excess and obsolete" ones, and coordinate efforts to keep them "out of the hands of terrorists".
The possession of the shoulder-fired missiles in the hands of criminals or terrorists pose a threat to both passenger and military aviation, a White House statement said.
Approximately one million of these weapons have been produced worldwide, an thousands may now be in the hands of "non-state actors," the statement said.