Much of the EU's gas supply from Russia comes via Ukraine
Russian gas giant Gazprom says it can no longer depend on Ukraine as a transit route to the EU and is looking to develop alternatives.
In a BBC interview, the deputy chairman of Gazprom, Alexander Medvedev, said he hoped EU countries would back the move.
Gazprom cut off Ukraine's gas supply on Thursday in a row over payment.
The firm has since accused Ukraine of stealing gas, however Ukraine's state energy firm said Russia was not sending enough gas to ensure the EU supplies.
Ukraine's state gas company, Naftogaz, denied illegally siphoning Russian gas, saying it was ensuring the export supply.
Ukraine has insisted it will not interfere with gas transported from Russia to other states via its pipelines, as it has enough gas in its reserves to look after its own needs for some time.
Hungary and Poland said pressure on their pipelines had dropped.
Naftogaz said earlier it was diverting some gas to maintain pressure in the pipeline network.
In his first foreign interview since the gas was cut off to Ukraine, Gazprom's Alexander Medvedev dismissed the suggestion his company was deliberately picking a fight with Kiev.
Instead he said Gazprom was ready to end the dispute immediately - but there was no-one to negotiate with.
"We are ready to enter negotiations day and night, but they probably have other tasks than to solve this problem because they are not in Moscow," he said.
Mr Medvedev said Gazprom has gone out of its way to ensure supplies of gas to Europe are maintained.
He said the problem was not with Russia, but Ukraine, adding "that's why we believe it's necessary to develop, as soon as possible, alternative transit routes".
The alternatives he talks of are two new pipelines Russia is planning to build that will by-pass Ukraine on their way to Western Europe.
The Nord Stream gas pipeline would run under the Baltic Sea from Russia to Germany, and the South Stream link would pass under the Black Sea.
The BBC's Rupert Wingfield-Hayes in Moscow says this latest dispute is expected to give those Russian plans a significant boost.
The Czech Republic, which holds the rotating EU presidency, said it would call a crisis meeting of envoys in Brussels on Monday to discuss the row.
Pipes across Ukraine carry about a fifth of the EU's gas needs. A similar row between Gazprom and Ukraine at the beginning of 2006 led to gas shortages in several EU countries.