"The heads of the two governments expressed their high estimation for the current level of Greek-Russian cooperation in a variety of sectors," Peskov told reporters in Magnitogorsk, where Putin is on tour.
Peskov said that Papandreou expressed appreciation to the Russian side for its cooperation, via the International Monetary Fund (IMF) and expressed certainty that the temporary economic difficulties faced by Greece will be soon overcome.
In Athens, a government announcement said that the two leaders discussed significant matters concerning Greek-Russian relations.
The telephone call took place at the initiative of Papandreou, who conveyed the Greek government's and people's deep sorrow for the recent tragedy on the Volga River.
They discussed matters pertaining to bilateral cooperation, in such fields as technology, the defence industry and energy, and in particular the Burgas-Alexandroupolis oil pipeline, in which project the two countries' interest remains undiminished.
The premiers further discussed the economic crisis, and Putin expressed his support for the Greek government's efforts to take the country out of the crisis.
Papandreou, in turn, thanked Putin for Russia's stance on Greek issues in the IMF discussions.
The two prime ministers also discussed developmental issues as well as investments, in which there is Russian interest.
Papandreou and Putin expressed their strong desire for acceleration and further development of Greek-Russian relations, which the Russian prime minister has described in the past as "strategic".
The Greek premier further invited Putin to visit Athens at a time convenient to him.