Russia's gas giant, Gazprom, has threatened to cut off gas supplies to Ukraine if a new contract is not in place by the beginning of next year.
The proposed price hike comes at the start of winter
Ukraine receives heavily discounted gas from Russia, offsetting the price against fees levied for transporting Russian gas through its pipelines.
Gazprom says it will not compromise over its demand that Ukraine pays what it says are appropriate market rates.
The company says a three-fold increase is both overdue and justified.
Ukraine's economy is in a much better condition than five years ago, when the current contract was signed.
Ukraine has proposed paying market rates - but in phased increases over a period of time, rather than all at once, in the depths of Eastern Europe's bitter winter.
Gazprom has rejected this offer, and has received political backing from the very top. President Vladimir Putin intervened late last week to say that Russia would no longer subsidise Ukraine.
That led a top Ukrainian official to accuse Russia of economic blackmail.
Some Ukrainians believe their country is to be punished for the Orange Revolution, which brought a pro-Western government to power.
But most Western analysts believe that Gazprom is steadily increasing pressure on Ukraine in order to mount an attempt to take physical control of its vital pipeline network.
Eighty percent of Russia's gas exports pass through Ukraine, a crucial weak point in what is acknowledged to be a powerful lever of Russian foreign policy. Cutting off direct gas supplies to Ukraine could bring the country's steel industry to its knees - potentially forcing Ukraine to divert the gas flowing from Russia to Western, Central and South-Eastern Europe.
By upping the ante so dramatically now, Gazprom appears to be trying to get foreign governments on side.