The Ukrainian MPs are expected to hold meetings with Russian State Duma Speaker Boris Gryzlov, Federation Council Chairman Sergei Mironov and other Russian officials.
Russian President Dmitry Medvedev said on Wednesday Ukraine must pay its natural gas debt to Russia in full or otherwise Kiev could face disruptions in supplies.
"The debt should be paid to the last ruble if they do not want the economy to suffer from Russian sanctions. The situation cannot be tolerated any longer," Medvedev said in an interview with leading Russian television channels.
Ukraine was reported to owe Russia more than $2 billion for the supplied gas. Russian energy giant Gazprom earlier threatened to cut off supplies at the start of 2009 as new contracts cannot be signed as long as the debt is outstanding.
Gas talks between Russia and Ukraine have been closely watched by European countries, which import a quarter of their gas needs from Russia. Ukraine transits about 80% of Russian gas bound for Europe.
"We are not pursuing a goal of cutting off supplies," Medvedev said. "But if Ukraine fails to pay, we will use a whole arsenal of measures, there must be no illusions on this score, but we will fulfill our obligations to consumers in other countries, including Europe."
The 2006 gas row between the two former Soviet states resulted in a brief cut in supplies to Ukraine and shortages were reported in Eastern Europe.