KIEV - Ukrainian state-run energy firm Naftogaz on Monday said it had filed a lawsuit at the Stockholm arbitration court to contest the pricing of natural gas it imports from Russian giant Gazprom.

"The lawsuit also contains a requirement to recover an amount of money from Gazprom, which Ukraine has overpaid since 2010," Naftogaz said in a statement.

The Ukrainian company estimates it has "overpaid" around 6 billion U.S. dollars to Russia due to the "unfair" gas contract.

Earlier in the day, Gazprom said it had filed a lawsuit at the Stockholm court demanding Ukraine pay off some 4.5 billion dollars of gas debt and decided to introduce the prepayment regime with Naftogaz.

The two sides have been locked in dispute for three years over a 2009 contract under which they agreed to tie the price of gas to the international spot price of oil.

Russia initially demanded Ukraine pay 485 dollars per 1,000 cubic meters of gas. Moscow then offered to remove an export duty, which would cut the price by 100 dollars. Ukraine had been holding out for a price of just over 268 dollars.

On Friday, Ukraine said it was ready to pay 326 dollars for the next 18 months while the two sides worked out a long-term price deal, but the two neighbors failed to reach a compromise during their weekend talks.