Gazprom CEO Alexei Miller met with Oleh Dubyna, head of Ukraine's Naftogaz, in Kiev.
"Oleh Dubyna said Russia is transiting more gas across Ukraine's territory than planned," the press service of the Russian state gas monopoly said.
Miller confirmed to Dubyna that in 2008 Ukraine will receive the exact volume of gas stipulated in the current agreement.
The company chiefs also met with Ukrainian Prime Minister Yulia Tymoshenko to discuss preparations for a long-term contract on gas deliveries to Ukraine during and after 2009.
Last Friday, Gazprom said Naftogaz had stopped tapping Russian gas in excess of a standing contract, and that the Ukrainian company had complied with Gazprom's demand to stay within the contract-mandated quotas for 2008.
Naftogaz and Gazprom signed a contract in March setting the price for Central Asian gas supplies to Ukraine for 2008 at $179.5 per 1,000 cubic meters, for a total volume of 49.8 billion cu m.
The price of the natural gas Russia sells to Ukraine, and the transit cost levied by Ukraine on Russian gas pumped to the European Union, have proved a major source of contention since Gazprom began hiking prices to the country in 2005 after years of subsidized supplies.
Ukraine, which transits about 80% of Russia's Europe-bound gas, threatened to start tapping fuel after Russia halved shipments to the country amid a dispute over Kiev's gas debt and supply scheme earlier this year.
In late February, Ukraine paid over $1 billion to Gazprom to clear its debt for 2007 supplies.