EU monitors had already begun arriving in Ukraine to oversee the flow of Europe-bound gas when the new dispute flared.
'Stipulations and additions'
The Reuters news agency reported that a declaration attached to the agreement by the Ukrainians stated that Kiev had not taken any transit gas and had no outstanding debts to Gazprom, the Russian supplier.
It also said Russia must supply extra "technical" gas to the Ukraine to maintain pressure in the pipeline system, despite the measure not being agreed with Moscow.
Russia cut off gas shipments that flowed through Ukraine more than a week ago after accusing Kiev of siphoning off supplies for its own use.
"I cannot call such stipulations and additions other than a mockery of common sense and violation of earlier achieved agreements"
"I cannot call such stipulations and additions other than a mockery of common sense and violation of earlier achieved agreements," Medvedev said.
A Russian government source said Vladimir Putin, Russia's prime minister, had proposed sending officials to the European Union in Brussels on Monday to discuss the deadlock, that has disrupted gas supplies to 18 European countries at the height of a bitter winter.
Mirek Topolanek, the prime minister of the Czech Republic, which holds the rotating EU presidency, told Putin that the Ukrainian additions were non-binding, a spokesman for the Russian premier said.
"Ukraine's declaration is not part of the [main] protocol and only represents the opinion of the Ukrainian side," the spokesman quoted Topolanek as saying during a telephone conversation.
The dispute first broke out when Moscow and Kiev failed to agree on the price for gas for the coming year.
Russia had insisted Ukraine pay current market rates instead of subsidised prices introduced during the Soviet era.
The two countries have also clashed over Ukraine's efforts to join Nato.
Europe receives one quarter of its gas from Russia, 80 per cent of which passes through Ukraine.