Kiev initially opposed holding talks in Russia, and suggested that the summit be held in a third country instead.
The renewed attempt to resolve the dispute comes after the EU on Wednesday threatened court action unless a solution was promptly found.
EU's call came a day after Russian gas exports to Europe came to a halt again in view of fresh differences between Russia and Ukraine.
Under a EU-brokered deal, Russia had resumed gas supplies on Tuesday only to shut them off again hours later.
Gazprom, the Russian national energy provider, claimed that Ukrainians were refusing to allow gas transit under conditions laid down by the deal.
Naftogaz, the Ukrainian state-run gas company, said they would not resume deliveries due to "impossible" transit conditions set by Gazprom.
The dispute has damaged the reputation of both Russia and Ukraine as reliable energy partners, underscoring Europe’s energy dependence on Russia.
More than 15 countries have been hit by the shutdown and hundreds of thousands of Europeans have been suffering in bitter winter conditions without heating.
Russia is the world's biggest natural gas producer and provides about a quarter of the gas used in the European Union - about 40 per cent of the gas the bloc imports.
About 80 per cent of the imports pass via pipelines in Ukraine.