Ukraine and Russia say they have reached an agreement on natural gas prices for this and next year, although they have not given any details.
Mr Yanukovych (right) is seen as an ally of Russia
Newly-appointed Ukrainian Prime Minister Viktor Yanukovych discussed the issue with his Russian counterpart Mikhail Fradkov.
Mr Yanukovych said prices would be "market-based" and "transparent".
In January, Moscow briefly cut off gas supplies to Ukraine which had a knock-on effect in Western Europe.
The dispute was resolved when Ukraine agreed to pay $95 (£50) per 1,000 cubic metres of Russian natural gas which was about double the preferential price it had paid before.
After talks on Wednesday in the Russian Black Sea resort of Sochi, Mr Yanukovych said the prices until the end of 2006 and for 2007 had been determined.
"The prices will be based on a market framework and the mechanism for their calculation will be transparent and will correspond to the level of economic relations between Ukraine and Russia," Mr Yanukovych said.
Mr Fradkov indicated that the January agreement was at the centre of the new arrangement, which makes it likely that prices will continue at the current level.
The trip to Sochi is Mr Yanukovych's first visit abroad since he became prime minister earlier this month in an alliance with his pro-Western arch-rival, President Viktor Yushchenko
Russia backed Mr Yanukovych in 2004's fraud-marred presidential election which led to mass street protests.
In March's parliamentary election, Mr Yanukovych stood on a platform of making Russian a second official language and opposing eventual Nato membership for Ukraine.
But Mr Yanukovych had to agree to tone down his pro-Moscow policies in the deal to receive the prime-ministership.
He now says he wants closer links with the West.
He also says Ukrainian children should learn good Ukrainian, calls for Ukraine to "truly move" towards Nato and has set the ambitious goal of joining the World Trade Organization by the end of this year.