In televised remarks made on 31 December, Putin ordered Russia's state-owned natural-gas monopoly Gazprom to supply Ukraine with natural gas at the current price for three months -- if Kyiv immediately agrees to pay higher prices starting in April.
Ukraine has until the end of 31 December to respond to the offer.
Gazprom has threatened to shut off supplies to Ukraine at 10 a.m. on 1 January if Kyiv does not accept Russia's decision to more than quadruple prices.
Gazprom wants Ukraine to pay world-market rates for the gas -- $230 per 1,000 cubic meters -- rather than pay, as it currently does, $50. Ukraine wants any increase to be phased in gradually.
In an interview aired on Ukrainian television on 30 December, Ukrainian President Viktor Yushchenko also questioned the size of the increase proposed by Russia. "Why Ukraine should pay $230? Why should the Baltic countries pay $120, Belarus $46.68, Turkey $100, Caucasus republics $100-110?" he asked. "Why should Ukraine, which is located closer than any of these countries to Russia and so the distance to transport gas is shorter, pay $230?"
On 31 December, Yushchenko offered some words of compromise, saying that "politically both sides are correct." However, he said that the two countries need to make their relations more "orderly" and that "we need to leave the period of feudalism behind. Only then we will be honest to each other."
The Ukrainian leader said there was "no need for ultimatums, no need to demonstrate political or economic pressure," adding that "I don't believe and I don't want to believe that [the dispute] is a form of pressure by Russia. I don't want to believe in it because it is a humiliating form of relations for us as partners."
Yushchenko nonetheless indicated that he believes Russia was seeking to exert influence over Ukrainian politics, saying that "I think this issue is clearly connected with the upcoming elections in Ukraine."
Yushchenko on 30 December handed control of Ukraine's energy sector to an ally of his bitter, pro-Moscow rival in presidential elections in late 2004, Viktor Yanukovych.
Vitaliy Hayduk, 48, had served as deputy prime minister in charge of energy and industrial affairs when Yanukovych was Ukraine's prime minister.
Yushchenko said he wanted Hayduk to ensure that Ukraine becomes self-sufficient within four years.
President Putin earlier this week described the gas dispute between his country and Ukraine as a "crisis" and offered to loan Ukraine several billion dollars to pay for the gas. Ukraine quickly rejected the offer.
Similarly, counterproposals made by Ukraine have been quickly dismissed by the Russian government and by Gazprom officials.
The European Union, which gets some 25 percent of its gas from Russia, has called an emergency meeting for 4 January to discuss plans for handling a possible disruption of supplies to the west because of the Russia-Ukraine dispute.