Chief executives Alexei Miller and Paolo Scaroni outlined preliminary terms for a future agreement and said the further development of long-term partnership had bright prospects in terms of joint projects.
"The meeting was held in a positive atmosphere, but we have signed no contract because it was only a stage of long-term talks," Scaroni told journalists after the meeting.
Earlier Friday, a Gazprom vice president met with the head of another Italian energy company, Edison, which annually buys 2 billion cubic meters of gas from Promgas, a Gazprom-ENI joint venture.
The talks come as a jittery Europe is looking to reduce energy dependence on Russia and diversify its energy supplies and sources in the wake of a dispute between Ukraine and Russia in January, which resulted in a supply shortfall. Moscow then accused Kiev of siphoning Europe-bound Russian gas.
Italy is the third largest European natural gas market after the United Kingdom and Germany. The share of natural gas on Italy's energy balance is over 30%, and imports, mainly from Algeria and Russia, accounted for some 86% of the country's natural gas demand last year.
Europe's second largest importer of Russian natural gas, Italy buys the fuel from Gazprom under five long-term contracts. In 2005, the country received 21.85 billion cubic meters.
In February 1998, Gazprom and ENI signed a strategic cooperation agreement which made them partners in the Blue Stream project, a major gas pipeline to provide direct supplies of Russian natural gas to Turkey across the bottom of the Black Sea. The companies established a joint venture, Blue Stream Pipeline Company, to provide finance, and conduct construction and maintenance work for the project. Put into operation in February 2003, the Blue Stream has to date supplied Turkey with 7.8 billion cu m.