Alexander Medvedev, deputy chief executive officer at Gazprom, said Ukrainian energy company Naftogaz took on 455 billion cubic feet of natural gas last year, but was contractually obligated to 1.4 trillion cubic feet.
"Gazprom on Wednesday billed Naftogaz of Ukraine $11.38 billion for gas shortfall in 2013 under the take-or-pay contract," the Gazprom deputy said.
Ukrainian Energy Minister Yuri Prodan said earlier this month the government may challenge a 2009 contract between Naftogaz and Ukraine to an international court of arbitration.
Gazprom in 2009 cut gas supplies to Ukraine because of contractual disputes. The deal that ended the dispute saddled Ukraine with some of the highest gas bills in the region.
European consumers get about of the quarter of their gas needs met by Gazprom, though the bulk of those supplies run through the Soviet-era gas transit network in Ukraine.
In mid-April, Russian President Vladimir Putin warned European leaders the region's energy security was at risk because Ukraine couldn't pay its bills.