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LONDON — Gazprom, the natural gas giant 50.01 percent owned by the Russian government, keeps ratcheting up the bill for Ukraine, increasing the economic pressure on Kiev in tandem with military pressure along Ukraine’s eastern border.

What Gazprom executives now say Ukraine owes them comes to more than $22 billion. In early March, Gazprom put the bill at less than $2 billion. How Gazprom now calculates its charges explains a lot about the way the company is used by the Kremlin for political purposes.

Behind the payment demands was a warning that Gazprom would cut off gas supplies to Ukraine, which it has done at least twice before, in 2006 and 2009, over political and financial disputes. And behind that warning is one to European countries that largely depend on Russian gas supplies moving through Ukraine.

In its annual report, Gazprom said that it might cut gas supplies to Ukraine unless its bills were paid, and that Europe could suffer reduced deliveries as a result. Ukraine has threatened to take Gazprom to court over what it said were inflated prices for gas.

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Gazprom’s chief executive, Alexei Miller, escaped the U.S. sanctions list for Russians involved in the Ukraine crisis as a political concession to European countries that depend on the company’s gas supplies.

In 1989, Gazprom was created out of the Soviet Ministry of Gas Industry. And unless there was a clear invasion of eastern Ukraine by the Russian military, senior European officials said, the European Union was unlikely to push for harsher sanctions or punish Gazprom.

Late last month, Gazprom sent executives to countries like Germany to argue its case for collecting what they said Ukraine owes. Alexander Medvedev, the second in command at Gazprom, said that his company had done everything possible to keep gas flowing to both Ukraine and Europe, but that the time of reckoning was near, and that Ukraine owed them $18.5 billion.

But in early March, Miller said that Ukraine owed just $1.89 billion for unpaid gas. Medvedev said recently that the figure was $2.2 billion, and that Ukraine had stopped payment altogether after Gazprom raised the price of gas on April 1 to $385 for 1,000 cubic meters, the standard measure for gas in Europe. That figure was up from $268, an increase of about 44 percent. The debt will reach $3.5 billion by mid-May, Medvedev said.

The sharp increase was political.

The reduced price was part of a pact Russian President Vladimir Putin struck in December with the former president of Ukraine, Viktor Yanukovych, for turning down a EU free-trade deal. Gazprom also paid Ukraine in advance for transit fees.

But after Yanukovych fled Ukraine in February, Miller announced that the price would revert to $385 per unit on April 1. Miller said Ukraine’s unpaid debt to Gazprom — and not any political motivation, like punishing and further destabilizing the European-minded interim government in Kiev — had prompted the move.

Then the price went up again.

Under a 2010 accord between Yanukovych and Moscow, Ukraine received a 30 percent discount on gas in return for extending Russia’s lease on its base in Crimea for the Black Sea fleet. But after Russia’s annexation of Crimea, Moscow abrogated the accord, canceling the reduction and bringing the price Ukraine now pays Gazprom to $485 per unit.

Gazprom added that it intended to apply this price retroactively to 2010 when the deal was struck.

That’s not all.

Medvedev, Gazprom’s No. 2 official, insisted that Ukraine owed an additional $18.5 billion (mostly for gas never used). This figure stems from a January 2009 contract that the prime minister at the time, Yulia Tymoshenko, signed after Russia cut off gas to Ukraine, again over unpaid debts (then some $2.4 billion).

The agreement eliminated a shadowy intermediary company, but committed Ukraine to a 10-year deal at a high level of consumption — about 50 billion cubic meters a year — and at a price higher than what the rest of Europe was paying.

But Ukraine’s gas consumption declined from 44 billion cubic meters in 2011 to 32 billion in 2012 and some 28 billion last year, given the recession, said Dmitry Petrov, an analyst of emerging markets at Nomura. Gazprom insists it should be paid for the difference.

In January, Gazprom demanded the additional $7.1 billion under the contract as payment for unused gas for 2012, but Ukraine refused to pay it, and it is considered unlikely to be enforced in any court outside Russia itself. Now Gazprom has billed Ukraine for an additional $11.4 billion for unused gas in 2013 under the same contract, including the retroactive pricing after 2010 that represents the return of prepayment on the base lease.

That would bring the total Gazprom says it is owed to at least $22 billion by the end of May.

But Gazprom isn’t done. It now insists on prepayment by Ukraine of a further $4 billion to $5 billion to buy gas to put into underground storage facilities for itself and especially for European customers of Gazprom next winter.

The deadline for Ukraine to pay up was Wednesday.

By May 16, he said, Gazprom would bill Ukraine for gas to be supplied in June, which must be paid for by the end of May to ensure delivery.

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