The conversation should have taken place on Saturday after a prisoner exchange of some 70 people between the two countries took place. The exchange of prisoners is seen as a great success for Ukraine's new president.
A statement from the Ukrainian presidential office states that "the presidents also agreed to hold discussions on organizing a meeting in the near future for the Normandy format" in the near future. The format means that France and Germany also participate.
Vladimir Putin stressed the importance of getting to a meeting shortly in a statement from the Kremlin.
Since Volodymyr Zelenskyj was elected Ukraine's new president in April this year, efforts to harmonize the country's relationship with Russia have intensified.
At the same time, the armed conflict in eastern Ukraine is ongoing between Russian-backed separatists and the Ukrainian military, which began in 2014 when Russia annexed the Crimean Peninsula.