Sergei Lavrov and Sergei Shoigu were set to visit Istanbul on Sunday - a meeting agreed by Turkish President Recep Tayyip Erdogan and his Russian counterpart, Vladimir Putin, foreign ministries in both countries said on Saturday.
But the Turkish ministry said on Sunday the two sides had decided instead to remain in touch for now.
Foreign Minister Mevlut Cavusoglu and Lavrov agreed in a phone call Sunday that contacts would continue in the coming period and that "meetings at ministers' level will take place at a later date".
Turkey and Russia - whose leaders have forged a strong partnership in recent years - support opposing sides in Libya, which has been riven by unrest since the fall of dictator Moamer Kadhafi in 2011.
Russia, along with the United Arab Emirates and Egypt, has backed eastern strongman Khalifa Haftar.
Turkey, together with regional ally Qatar, supports the UN-recognised Government of National Accord (GNA) in Tripoli.
In Syria, Turkey and Russia say they are working to bring a political solution to the conflict.
Iranian Foreign Minister Mohammad Javad Zarif was expected to visit Istanbul on Sunday ahead of talks with Turkish officials on Monday, a Turkish diplomatic source said.
While Iran and Russia back Syrian President Bashar al-Assad, Turkey supports rebels seeking his overthrow.
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