Gazprom, Kommersant reported, rejected the Ukrainian government’s argument that gas delivered to rebel territory could not be counted against its prepaid volumes, at least because Naftogaz, the state energy company, could not send meter readers to the two border crossing points, Prokhorov and Platovo, to confirm deliveries.

As the gas Ukraine had already paid for flowed into their territories, separatist leaders went on local television to thank Russia and Mr. Putin. “We thank the Russian Federation and Vladimir Vladimirovich, as Russia is again extending its hand to help, giving warmth,” said the leader of the Luhansk People’s Republic, Igor Plotnitsky. “Thank you, Russia.”

Mindful of how Russia has used gas as a political weapon, Ukraine has taken strong steps in recent months to reduce its dependence on it. Ukraine and Slovakia reached a deal for reverse piping of gas already purchased in Europe, and a separate deal to buy gas from Norway.

And despite Mr. Miller’s comments, there was no reason to believe that Europe would find itself short of gas as a result of the dispute. Europe, too, has reduced its dependence on Russian gas by engaging other suppliers, and in recent months has built up reserves in anticipation of potential difficulties with Russia.

Russia, while controlling the supply, is in turn dependent on Ukraine to allow gas through its pipelines to other customers in Europe. Painfully aware of that reliance, Russia has sought to cut Ukraine out by building a new pipeline under the Black Sea and through Turkey.

The continuing gas dispute demonstrated the extent to which Ukraine would still be at Russia’s mercy even without the war against Russian-backed separatists. Fighting, however, has continued despite the cease-fire brokered this month in Minsk, Belarus, and on Tuesday, the foreign ministers of Russia, Ukraine, France and Germany met in Paris in a bid to get it back on track. It did not appear that they had much success.