During his official visit to Cyprus, Tsipras said that the two countries must work together to develop "a bridge of peace and cooperation between Europe and Russia," the Cyprus Financial Mirror newspaper reported.
The prime minister said that Athens does not consider loans from Russia to be a possibility.
Relations between Moscow and Brussels significantly deteriorated following Crimea's reunification with Russia in March 2014. The EU, the United States as well as a number of other countries imposed several rounds of economic sanctions against Russia, accusing it of interfering in Ukraine's internal affairs.
On Sunday, European Parliament President Martin Schulz expressed concern over the new Greek government's pro-Russian stance. Members of the left-wing Syriza party, having recently won parliamentary elections, have repeatedly criticized the West's sanctions against Russia, saying that they damage the Greek economy also, particularly agriculture.