"We are paying money gradually now," he was quoted as saying Saturday by ITAR-Tass.
Stavitsky didn't indicate how much was paid toward the debt or how much debt was incurred.
European consumers get about 20 percent of their natural gas needs from Russia, most of the gas running through a Soviet-era gas transmission network in Ukraine.
Gazprom cut gas supplies to Ukraine briefly in 2009 over debt issues.
Ukraine, a former Soviet republic, has struggled with paying its gas debts to Gazprom
In December, Russian President Vladimir Putin said Ukrainian energy company Naftogaz can pay $268.5 per 1,000 cubic meters of natural gas, the standard purchase volume, instead of the regular rate of $400.
Putin said the decision was only a temporary measure meant to ensure consumers in Europe have a secure supply of natural gas. The decision followed Ukraine's move to suspend free-trade talks with the European Union, saying it needed to protect its economic ties to Russia.