The two leaders held talks over telephone Wednesday, Kremlin press service reported.
"The US president congratulated Putin on his inauguration. Putin and Obama exchanged greetings on the Day of Victory over fascism, noted the historic significance of the allied relations that linked our peoples during the World War II and gave best wishes to the veterans," the report added.
"During the conversation heads of states discussed the prospects for Russian-American relations and personal contacts," it added.
According to the press service, the conversation "went in a constructive spirit."
Putin was forced to step down in 2008 by a constitution that forbids more than two subsequent terms, but is silent on further periods in office. He shifted to the post of prime minister after installing his hand-picked successor, Dmitry Medvedev, in the Kremlin, but remained by far Russia's most powerful politician.
He won a landslide victory in the March 4 presidential elections marred by allegations of vote fraud