Fernandez was inaugurated on Monday, taking over the presidency from her husband Nestor Kirchner. She pledged to continue her predecessor's reforms that brought relative economic stability to South America's second largest economy following the acute crisis six years ago.
"We value friendly relations with Argentina," Putin said in his message, highlighting the two nations' common approach to fighting terrorism, organized crime, drug trafficking and other challenges.
Putin also called for economic ties to be strengthened by high level of political cooperation, and highlighted joint projects in space, nuclear power, telecommunications, and energy.
Fernandez won 40% of the vote at the presidential election in November, 10% more than her closest rival. She was previously senator for the province of Buenos Aires.
Fernandez is believed to have contributed substantially to her husband's election as president, as she led his campaign in 2003.
Argentina's first female leader was Isabel Peron, who took power in 1974 after her husband Juan Peron died. She was deposed by a coup in 1976. Isabel Peron was briefly arrested in Spain in March this year on charges she approved right-wing death squads during her time in power.
As president, Nestor Kirchner entrusted his wife to conduct crucial talks, including with Venezuelan President Hugo Chavez.
His wife's presidential program includes maintaining good relations with Chavez and another fighter against "American imperialism," Bolivian President Evo Morales.
Fernandez is frequently compared to Eva Peron, a wife of Argentinean President Juan Peron - although Eva was not a president, unlike Juan's last wife, Isabel - as well as to Hillary Clinton.
However, Argentina's new president does not appreciate the latter comparison. "Hillary has become famous because her husband was president. That is the main difference between us. Our society needs women; there must be more of them in the country's leadership," she said earlier.
