Mr Obama's meeting with the man widely regarded as the most powerful in Russia is taking place on the second day of the American leader's visit to Moscow.
The US president said Mr Putin had done extraordinary work as both president and prime minister.
On Monday, Mr Obama and Russian President Dmitry Medvedev signed eight separate agreements.
They included a pact to negotiate a new arms control treaty to replace the 1991 Start I pact which expires in December.
A new agreement could see the two countries reducing their nuclear warheads by up to the third, to below 1,700 each within seven years of the treaty's signing.
'Old ways'
Also on Tuesday, Mr Obama is due to deliver a major speech on democracy, the global economy and the US-Russian relationship.
Mr Obama said last week that he thought Mr Putin, the former Russian president turned prime minister, had "one foot in the old ways of doing business and one foot in the new".
Mr Putin responded: "We stand solidly on our own two feet and always look into the future."
But on Monday, the US leader struck a more diplomatic tone.
"My interest is in dealing directly with my counterpart, the president [Medvedev], but also to reach out to Prime Minister Putin and all other influential sectors in Russian society," Mr Obama was quoted as saying by Reuters news agency.
A BBC correspondent at Monday's talks said the two presidents seemed to have taken a significant step towards improving US-Russian relations, which have been badly strained in recent years.
Separately, Russia also agreed to allow the US military to fly troops and weapons across its territory to Afghanistan, allowing it to avoid using supply routes through Pakistan that are attacked by militants.
However, on the contentious issue of US plans to base parts of a missile defence shield in Eastern Europe, the presidents merely said they had agreed to a joint study into ballistic missile threats and the creation of a data exchange centre.
