* Ukraine says stops buying Russian gas for storage
* Medvedev tells Gazprom to stop advance fee payments
* Ukraine's Naftogaz says fees and gas prices linked
(Recasts with Tymoshenko, Kremlin comments)
By Dmitry Zhdannikov and Pavel Polityuk
MOSCOW/KIEV, Sept 7 (Reuters) - Ukraine has sufficiently healthy volumes of stored natural gas to ensure smooth transit to Europe this winter so it will stop buying Russian gas for storage, Prime Minister Yulia Tymoshenko said on Monday.
Her comment will be met with relief across the continent, which experienced a two-week stoppage of a fifth of its gas supplies last January following a dispute between Moscow and Kiev over payments.
The reassurance comes after Moscow had warned for months that Kiev was slow in building up its stocks for winter exports.
"With 25.5 billion cubic metres of gas held in underground storages, we can cease storing gas. We have established that 25.5 bcm is enough to ... guarantee reliable export of Russian gas to the European Union," Tymoshenko told reporters.
Tymoshenko, the most popular Ukrainian politician now in office, wants to avoid a new gas row with Russia in the run-up to a presidential election on Jan. 17, in which she has said she would run.
Last week she clinched a deal with her Russian counterpart Vladimir Putin, who allowed Ukraine to import much less gas than previously agreed, saving Ukraine's strained economy from potential big fines. [ID:nL1716728]
Tymoshenko's warmer ties with Russia over recent months have prompted speculation that Moscow may be backing her in the election to gain influence over the former Soviet republic.
On Monday, Russian President Dmitry Medvedev also praised Ukraine for timely payments for gas supplies in the past months.
"The fact that our Ukrainian partners are paying is a good sign. This is a sign that they are following the agreements as it should be," he told the chief executive of Russian gas export monopoly Gazprom (GAZP.MM) Alexei Miller.
But Medvedev also told Miller his firm should stop making advance payments to Kiev of the transit fees it pays to send its gas to Europe through pipelines across Ukrainian soil.
This was because the agreement reached in January, which settled the row between Kiev and Moscow, did not make provision for payments in advance.
The Kremlin transcript quoted Miller as telling Medvedev that transit fees to Ukraine had been pre-paid until the end of the first quarter of 2010 - the moment when Ukraine will have a new president.
"As far as the idea of pre-payment of tariffs is concerned, I want to ask you a simple question: has the (January) agreement been revised?" Medvedev asked Miller. Miller said it had not.
"Then don't pay," Medvedev said. "We need to act in line with the agreement which was reached...We are also facing not the easiest times now," Medvedev added.
The official Kremlin transcript contradicted an earlier report from Interfax news agency, which said Medvedev had told Miller not to agree to change gas transit fees. [ID:nL7602291]
That would have been surprising as Moscow and Kiev have reached many compromises in the past weeks and their comments on fees only slightly differed last week. [ID:nL325489]
Ukrainian state energy firm Naftogaz said on Monday that according to the January deal, the transit fees that Gazprom must pay were subject to an annual change and directly linked to the import price of gas used for transit.
Last week, Gazprom said it expected gas transit fees via Ukraine to rise by up to 59 percent in 2010, a similar figure to Ukraine's expectations of a maximum 60 percent increase. (Writing by Dmitry Zhdannikov; editing by Anthony Barker)