"Begin an appropriate procedure," Medvedev was quoted as saying at a meeting with Alexei Miller, the head of Russian gas giant, Gazprom, in Moscow on Monday.
Gazprom said last week that Belarus owed it $192m in unpaid debts and gas exports
would be reduced from 0600 GMT on Monday if the debt was not settled by then.
Belarus has challenged the Russian claim and refused to pay.
A source in the Belarussian government, who spoke on condition of anonymity, said European gas deliveries could be affected if supplies to Belarus are disrupted.
European worry
Russia's gas price disputes with its neighbours became a worry for Europe when its supplies were halted for almost two weeks in the winter of 2009 while Russia and Ukraine argued over prices and transit terms.
Any cuts, especially if they affect supply beyond Belarus, could further damage Russia's reputation as a reliable exporter at a time when Gazprom is facing falling demand from crisis-hit Europe and competition from US-produced shale gas.
A cut in supply to Belarus, however, would not affect Europe as much as the 2009 standoff because only about a fifth of Russia's gas exports to Western Europe go through Belarus with the rest going through Ukraine.
Seasonal demand is also much lower than in the winter when the 2009 disruption took place.
Energy experts agree that a worst-case scenario of seriously damaged supplies to Europe is unlikely as Gazprom can re-route gas deliveries to Europe to avoid Belarus.
Analysts say Poland can import Russian gas via Ukraine and Germany can receive it through Ukraine, Slovakia or the Czech Republic.
