In a meeting with Putin, Prime Minister Dmitry Medvedev said Kiev has asked to extend the deal signed in October which expires at midnight. "Let's do it," Putin responded.
He said the deal "would be active for another three months" after which Russia will review it taking into account the "volatile oil prices on global markets."
Russia's energy minister Alexander Novak said earlier this month that the price Moscow is setting for Ukraine will be USD 348 per 1,000 cubic metres starting on April 1. The deal then lowers the price by USD 100 in what Moscow calls a discount.
Moscow had then withdrawn the discount it had offered Ukraine after a pro-Western government took over in Kiev last year following the overthrow of pro-Russian Viktor Yanukovych.
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Cash-strapped Ukraine has been pre-paying for Russian gas it gets as required by the October agreement, but only in increments of a few days at a time.
Ukraine's gas operator Naftogaz had asked to extend the deal to spring 2016, and Brussels has also indicated the need for a long-lasting solution to the dispute.
The European Union receives about a third of its gas from Russia, with half that amount transiting via Ukraine pipelines.
Talks between Russia, Ukraine and the European Union are set to resume in Berlin in mid-April.