The deals run counter to claims by the Hungarian Prime Minister, Ferenc Gyurcsany, that he is a firm supporter of a European Union-sponsored gas pipeline project. The project, called Nabucco, is considered a competitor to a Russian-backed project, called South Stream, in which Moscow has both economic and political interests.
One of the deals, signed in Moscow last week in the presence of Mr. Gyurcsany and Prime Minister Vladimir Putin of Russia, calls for the Hungarian government and the state-owned Hungarian Development Bank to finance the South Stream pipeline project on Hungarian territory.
South Stream is a joint venture between Gazprom, the Russian state-controlled energy giant, and the Italian energy company Eni. It will run under the Black Sea and link Russia directly to Bulgaria, bypassing Ukraine, through which more 80 percent of Russian gas is sent to customers in Europe.
Little progress has been made on the pipeline, which is not thought to be ready until at least 2015.
Estimates of the cost of South Stream vary. Mr. Putin said last week the sum would be around € 10 billion, or $ 13 billion. Russian President Dmitry Medvedev, who has questioned whether the project should go ahead, told investors last month that it could cost as much as € 20 billion.
South Stream's northern branch would run from Bulgaria to Serbia, Hungary and Austria.
The 3,000 mile, or 1,865 mile, Nabucco pipeline is to be completed in 2013 at an estimated cost of € 8 billion. It is supposed to bring natural gas to Europe from Azerbaijan and eventually Iran.
Doubts have grown about the feasibility of Nabucco because of uncertainty over both the source of the natural gas and the level of public financing available amid the recession sweeping Europe. Hungary received a € 25 billion rescue package from the International Monetary Fund and the EU in October.
Mr. Gyurcsany agreed nearly two years ago to support Gazprom's plans to build South Stream, saying he saw no conflict of interest in supporting both the EU and Russian pipeline projects.
For Russia, South Stream would reduce dependence on Ukraine, with which Moscow has ongoing political conflicts. It would also lock countries in Central and Southern Europe into long-term Russian energy contracts that would prevent them from diversifying their sources.
"This is all about weakening its dependence on Ukraine," said Peter Kaderjak, director of the Regional Center for Energy Policy Research in Budapest. "But it is also about Russia extending its economic, if not political, influence here in Hungary."
The other deal involves Gazprom and MOL, Hungary's oil and natural gas company, establishing a new gas storage site in Hungary. The new company will be owned equally by Gazprom Export and MOL and will have a capacity of 1.3 billion cubic meters, or 46 billion cubic feet, of natural gas.
MOL said Tuesday that the deal would increase Hungary's energy security as Ukraine became increasingly unreliable as a transit country for sending Russian gas to its customers in Eastern and Western Europe.
MOL recently sold its gas storage facility to the German company E.ON Ruhrgas and, according to analysts, now seeks to re-enter this sector to meet all its domestic needs in times of shortages and also supply natural gas to its neighbors.
Russia has its own interest in teaming up with MOL. In a bid to increase its dependence on Ukraine, Russia wants to build storage facilities in Europe, besides new pipelines that will bypass Ukraine.
Gazprom is building large storage units in Germany, Austria, and Hungary, and it plans to acquire a site in Slovakia.