Last week, Mr Medvedev warned Belarus that unless it paid off its gas debts within five days, it would face cuts.
Gazprom says Belarus owes about $200m (£134m; 160m euros) after failing to pay increased prices.
About a fifth of Europe's supplies of Russian gas is pumped through Belarus.
It was not clear whether the dispute would affect European customers or if Gazprom would be able to send more gas via Ukraine, said the BBC's Richard Galpin in Moscow.
Russia has started cutting gas supplies by 15% on Monday, gradually due to increase to more than 80% if there is no breakthrough in continuing negotiations between the two countries.
Gas supplies will be reduced "day-by-day, proportionally to the debt's volume", Gazprom's chief executive Alexei Miller said, according to Ria Novosti news agency.
Mr Miller said Belarus admitted having the debt.
"But it proposes to pay it with machinery, equipment and various other products," Mr Miller told Mr Medvedev on Russian television.
Mr Medvedev said foreign payments could only be accepted in foreign currencies: "Gazprom cannot accept debt repayments in anything, be it pies, butter, cheese or other means of payment."