Having failed to pay the debt, Ukraine no longer qualified for a reduction that Gazprom had offered the Ukrainian national energy company in December, Mr. Miller said. That price break was an incentive Moscow granted to Ukraine in return for its rejecting a free-trade pact with the European Union, a move that touched off the protests that eventually doomed the government of President Viktor F. Yanukovych.

“The December discount on gas cannot be applied,” Mr. Miller told reporters in Moscow.

The jump in the price came as no surprise to the new authorities in Ukraine. They have already planned, as required under an International Monetary Fund loan program, to slash state subsidies that have kept gas prices artificially low for consumers and industry.

Over the weekend, Secretary of State John Kerry and Russia’s foreign minister, Sergey V. Lavrov, failed to agree on a diplomatic solution to the crisis during talks in Paris. On Monday, however, Russia’s military withdrew a battalion of about 500 troops from the border with Ukraine, a mostly symbolic reduction in a force of about 40,000.

The army has said it is merely carrying out exercises, and Mr. Lavrov and other Russian officials have offered assurances that they do not intend to invade Ukraine. But President Vladimir V. Putin has said he will intervene to protect Russian speakers anywhere in Ukraine, if Ukrainian nationalists threaten them.

The gas price rise illustrated how, even if the Russian Army withdrew from the border, Russia would retain numerous economic weapons to wield against Ukraine, and it is widely expected to use them, deftly and unrelentingly, as it has for years.