Gazprom in 2009 cut natural gas deliveries through Ukraine after a series of contractual disputes. Kiev managed to break the impasse, though the government later sentenced former Prime Minister Yulia Tymoshenko to jail for abusing her authority in the deal.
Alexei Miller, the top executive at Gazprom, welcomed Boiko to his Moscow offices to discuss the terms of their relationship.
"The meeting discussed the cooperation progress of Russia and Ukraine in the gas sector," the energy company said in a statement.
Ukraine is eager to revise its contract with Gazprom because of the heavy financial burden. However, neither Gazprom nor the Ukrainian government announced any major breakthrough from the Moscow meeting.
Kiev announced recently that Chevron and Royal Dutch Shell were approved for the development of two shale natural gas fields in the country.
The U.S. Energy Information Administration estimates Ukraine has around 42 trillion cubic feet of shale gas reserves, putting it in the No. 3 spot among European countries.