The possibility of a new "gas war" between Russia and Ukraine inched closer on Tuesday, as the Russian state energy giant Gazprom complained that Kiev had outstanding debts of over half a billion pounds and demanded swift payment.

Gazprom's concern comes a month before Ukraine is due to sign up for closer ties with the European Union, a deal that has infuriated the Kremlin.

The complaint brought back memories of crises in 2006 and 2009 in which Russia turned off the gas to Ukraine, leaving many European nations that rely on pipelines passing through the country without energy in the middle of winter.

Russia wants Ukraine to join its own Customs Union of former Soviet states, and has repeatedly sent dire warnings that by signing the deal with Europe, Ukraine will lose billions of dollars and face myriad problems. One Kremlin economic adviser even predicted that if the deal is signed "political and social unrest" will ensue and Russia could cease to recognise Ukraine's status as a sovereign state.

"We are deeply concerned about the arrears accumulated by Ukraine for supplies of Russian natural gas," said Alexei Miller, Gazprom's chief executive, on Tuesday. He said the Russian side has made a number of concessions to Ukraine, including paying for transit of gas across it in advance, and giving discounts. Nevertheless, he said, Ukraine has failed to pay $882m (£550m) for gas deliveries that was due by 1 October at the latest. Miller said the current situation was "a dire state of affairs" and added the issue "has to be addressed and settled quickly".

Gas prices are a controversial issue in Ukraine, with the prime minister, Mykola Azarov, recently claiming that the country has overpaid by over $20bn over the past three years for Russian gas.

Former premier Yulia Tymoshenko was jailed for seven years in 2011 on charges of abuse of office, related to a gas deal she brokered with Russia in 2009 when she was prime minister. The current government says the deal forced cash-strapped Ukraine into paying unfairly high prices for gas.

Vladimir Zharikhin, deputy director of a pro-Kremlin thinktank on relations between former Soviet countries, denied that Gazprom's announcement was a political ploy designed to increase pressure on Ukraine not to sign the EU deal, and insisted that Ukraine had manufactured the dispute on purpose, in order to play the victim in Europe.

He said: "They were making the payments before, so why have they suddenly stopped? They want the EU to feel sorry for them, and to prove what a bad neighbour Russia is and how much pressure they are putting on poor Ukraine."

Ukraine is due to sign the association agreement on closer trade links with the EU at a summit in the Lithuanian capital Vilnius on 29 November, but European leaders have said several times that the deal will be possible only if Ukraine's president, Viktor Yanukovych agrees to release Tymoshenko from custody.

She is currently being held in a hospital in eastern Ukraine under prison guard. The case against her has been widely denounced as politically motivated.

A delegation of European politicians was expected in Kiev on Tuesday in the latest attempt to cement a deal on Tymoshenko. Yanukovych is reluctant to grant a pardon to his arch rival, but may allow her to leave Ukraine to receive medical treatment in Germany.

Russia has repeatedly warned Ukraine that the consequences of aligning with Europe will be painful, but despite Moscow's harsh rhetoric, it seems the Kremlin is resigned to seeing Ukraine slip out of its orbit. The focus now is on proving to Kiev what a terrible mistake it has made.

"To say we are dreaming of having Ukraine in the Customs Union, especially with the behavioural patterns of the current Ukrainian leadership, is not quite true," said Zharikhin, insisting the EU deal will prove far more damaging to Ukraine itself than to Russia. "They are very unreliable partners."