* Ukraine and Russia in arbitration court over gas supplies
* Gazprom concerned over level of gas in Ukraine's storages (Adds Naftogaz comments)
By Ivana Sekularac
BELGRADE, May 28 (Reuters) - Russian natural gas producer Gazprom put Ukraine's total gas debt at almost $29.5 billion on Thursday, ratcheting up pressure in a gas pricing dispute with the country, which is fighting a pro-Moscow rebellion on its eastern outskirts.
Ukraine's Naftogaz and Gazprom are squaring off in an arbitration court in Stockholm, where Naftogaz is seeking more than $16 billion from the Kremlin-controlled company.
Kiev is challenging the price of Russian gas, and billions of dollars in debts which Russia says have accrued, and is appealing to international arbitrators for a definitive ruling.
"The total debt of Ukraine until this date is $29.477 billion," Gazprom Chief Executive Alexei Miller told an energy conference in Belgrade.
Of that, he said, $2.6 billion is for gas deliveries in 2013 and 2014, $200 million was for gas deliveries to southeast Ukraine, and the rest was a fine for "take-and-pay", in which clients pay a minimum for a certain volume of gas whether they buy the whole consignment or not.
Naftogaz said in a statement the bills claimed by Gazprom under the take-or-pay stipulations contradict a 10-year contract signed in 2009. The company is also challenging the clause in the court.
Previous gas disputes between Ukraine and Russia have affected the European Union, where Gazprom meets a third of gas demand. Around 40 percent of that gas travels via Ukraine, which until recently bought most of its own gas from Russia.
Gazprom and Ukraine have agreed on the terms of Russian gas supplies to Kiev for the second quarter. Under this deal, Gazprom has dropped a take-or-pay clause.
Miller repeated his concerns about Ukraine's ability to fill its gas storage tanks to see the country and Europe through the winter.
"Ukraine is already pumping gas and storing gas for the next autumn/winter period. The speed and volumes they have today definitely will not allow Ukraine to pump a minimal volume ... which will allow it to cover by 100 percent without any risk, to live through a cold winter, by both Ukraine and the European countries," Miller said.
"There is only one conclusion. Ukraine has to increase the speed of the pumping and purchasing."
He also said Gazprom's gas exports to Europe would increase by 5 percent in 2015 from a year earlier. (Additional reporting and writing by Vladimir Soldatkin in Moscow and Natalia Zinets in Kiev; Editing by Susan Thomas and David Holmes)