Gazprom spokesman Sergei Kuprianov said negotiations are ongoing as to how and when the Ukrainian company will settle its outstanding debt obligations.
"There is a progress in the process of negotiations," he told state news agency RIA Novosti, noting Ukraine still owes for 347 billion cubic feet of natural gas.
Naftogaz avoided a switch to a pre-payment mechanism when it paid some of its debt to Gazprom last week, though the Russian side said it's still owed more than $2 billion.
Russian and Ukrainian negotiators met Monday with European Energy Commissioner Gunther Oettinger in Brussels to discuss the ongoing gas row. All three sides said there would be no interruption of gas deliveries, no switch to a pre-payment scheme in June and no international arbitration so long as talks are ongoing.
"The [top executives] of Gazprom and Naftogaz have developed an approach in which both companies will further consult and continue talks in the next days," a European statement on the talks read.
European consumers get about a quarter of their gas needs met by Russia, though most of that runs through the Soviet-era transit network in Ukraine.
Similar debt disputes in 2006 and 2009 saw Gazprom cut gas supplies through Ukraine and the political upheaval in Kiev last year has exposed European consumers to threats to their energy security.