"[Ukraine] has once again requested another deferral on historical debt and, still worse, on current payments," he was quoted by Interfax as saying Wednesday.
Ukraine, a former Soviet republic, last year secured some relief from its gas debt burdens following its November decision to suspend efforts to sign free trade and association agreements with the European Union.
Medvedev said the debt issue would be discussed with whoever replaces Ukrainian Prime Minister Mykola Azarov, who stepped down this week to ease Kiev's ongoing political crises.
Pro-EU demonstrators have strained the resolve of the current Ukrainian government.
The Russian leader said Kiev is ready to settle some of its debt, however, adding a new government in Kiev would change the situation "in a substantial way."
Russia in 2009 cut gas supplies to Ukraine briefly in response to contractual disputes. Most of the Russian gas for Europe runs through Ukraine's transit system and the 2009 disruption caused widespread downstream problems.