Spokesman Sergei Kupriyanov told RIA Novosti: "The situation must be resolved by Monday. If this does not happen, then on Tuesday we will halt supplies at 10:00 in the morning."
Ukraine's state-owned oil and gas company Naftogaz held talks in Moscow with Gazprom on the gas debt issue earlier in the day.
Kupriyanov said Naftogaz had shown unwillingness to discuss the gas debt.
The meeting with first deputy board chairman of Naftogaz, Igor Didenko, who held talks at Gazprom's headquarters, "showed Ukraine's unwillingness to hold meaningful discussions on this problem. Didenko was informed in detail of Gazprom's position, and the talks ended with this," Kupriyanov said.
Ukrainian Prime Minister Yulia Tymoshenko told national media Friday that Russia and Ukraine would negotiate to avoid a looming gas dispute.
On Tuesday, Ukraine's government had ordered the Foreign Ministry and Naftogaz to start talks on direct gas supplies from Russia, bypassing RosUkrEnergo, the intermediary company co-owned by Gazprom.
"Tomorrow we will begin telephone and face-to-face talks... I think we will try to clarify the situation, to understand what caused RosUkrEnergo's debt to Russia, what prevented them from paying it, and why they put Ukraine in a predicament like this," Tymoshenko was quoted by the UNIAN new agency as saying.
Tymoshenko said the crisis was prompted by a lack of direct dealings between Gazprom and Ukraine's Naftogaz: "More often than not, intermediaries like RosUkrEnergo disrupt both payment and gas supplies to Ukraine," she said, reassuring Ukrainians that, "Everything will be stable and secure."
Naftogaz said in a statement Friday that the company has no debts to Russia.
Ukrainian President Viktor Yushchenko said Thursday that Gazprom's behavior is merely a response to Ukraine's plans to raise transit tariffs and to remove intermediaries in gas deals.
RosUkrEnergo, a Swiss-registered trader, has been Ukraine's sole supplier of natural gas since 2006, when Moscow and Kiev resolved a pricing dispute that led to a brief halt in supplies affecting Europe-bound exports.
About 80% of the natural gas that Russia supplies to Europe is transited via Ukraine.
On February 5, Ukraine signed an agreement with the World Trade Organization in Geneva clearing the way for the country's membership to the global trade body in the summer. Experts say this could complicate Russia's gas talks with the country and its own WTO bid.