"We are sure that we will cope with the situation without any damage being caused to our gas transportation or production system," said Gazprom deputy CEO Alexander Medvedev.
He said Ukraine had shut down three of four pipelines that export Russian gas to Europe, severely disrupting supplies.
Medvedev said Ukraine had acted "irresponsibly" and urged Russia's "partners" to help solve the problem.
"We are meeting this challenge together with our European partners," Medvedev said. "This is a matter of unprecedented irresponsibility of a country across whose territory we deliver 80 percent of our gas to Europe."
However, the German economics and technology minister said Russia and Ukraine should settle their dispute between themselves and that Germany or the EU could not act as intermediaries in that situation.
"Germany and the EU are consumers of Russian gas that is supplied through Ukraine. But we are neither intermediaries nor even a party to the conflict," Michael Glos said, adding Kiev and Moscow should resume bilateral negotiations.
"I expect an immediate resumption of negotiations," he said in an interview with the Frankfurter Allegemeine Zeitung newspaper.
The EU has called the substantial cuts in Russian gas supplies to some member states "completely unacceptable."
Russian gas supplies through Ukraine to Bulgaria, Greece, Macedonia, Romania, and Turkey have been halted. The Apcom agency said Russian gas supplies to Italy were suspended in the early hours of Tuesday but then resumed.
Gas deliveries to the Czech Republic have fallen by 75%, while Poland could reduce gas supplies to its industrial enterprises following the Russian cuts of gas deliveries to Western Europe through Ukraine, a Polish deputy economics minister said.
Ukraine's state-run Naftogaz said earlier on Tuesday Gazprom had reduced deliveries of natural gas for transit through Ukraine to a third of their normal rate, which would affect Western European customers.
Naftogaz head Oleh Dubyna said Russia had probably decided to stop all gas supplies to Europe via Ukraine.
Gazprom said it would pump more gas through alternative routes via Belarus and Turkey to ensure European supplies were not affected.
The Russian energy monopoly said on Monday it would reduce its delivery of gas to Ukraine by 65.3 million cubic meters - the volume that had been stolen.
Gazprom's CEO Alexei Miller said that Gazprom was ready to guarantee deliveries to Europe by buying gas on the spot market, and that as well as increasing transit volumes through Belarus, Poland and Turkey, Gazprom would increase volumes of gas taken from underground reservoirs in European countries.
Gazprom cut off gas supplies to Ukraine on Thursday after last-ditch talks with Kiev on a new deal for 2009 and debt repayments failed late on New Year's Eve.
Around 80% of Russia's gas exports to Europe pass through Ukraine, and some European countries, including Poland, Hungary, Bulgaria, and Romania, have reported drops in Russian gas supplied through Ukraine's pipeline network.
Miller has accused Naftogaz of tapping Russian gas, which Ukraine denied, blaming Russia for creating the shortfall by deliberately cutting deliveries to Europe.
With Ukraine's gas debt to Russia from 2008 unresolved and no contract agreed for 2009 deliveries, the issue of Russian gas flowing through Ukrainian pipes to European consumers further west has become contentious.
In response to a claim by Ukraine's energy ministry, the Kiev economic court ruled on Monday that Naftogaz could not pump Russian gas westwards at a price of $1.6 for 1,000 cubic meters per 100 kilometers.
Both Gazprom and Naftogaz have said that they will file lawsuits with the Stockholm Arbitration Court, which deals with international commercial legal disputes. The court on Monday said it could not comment on whether it was considering lawsuits from either party in the gas dispute.
