Greece's political leadership met with Russian gas giant Gazprom head Alexei Miller on Tuesday to discuss bilateral cooperation in energy matters, with a focus on extending the so-called Turkish Stream natural gas pipeline to Greece.

The planned pipeline, which will transfer Russian gas from the Black Sea to central European markets, will be constructed through a joint venture with the participation of private funds and European companies under the EU's legislative framework, Miller said in statements to the press after meetings with Greek Prime Minister Alexis Tsipras and Energy Minister Panagiotis Lafazanis.

Gazprom's chief stressed that the project would greatly benefit all sides.

"Cooperation between Greece and Russia is of major importance for us. It is a strategic cooperation, in particular in the energy sector. The pipeline issue is among our top priorities. We continue talks and hope that very soon we will reach an agreement that will benefit our country, the economy and people," Lafazanis said on Greece's part.

The Greek official stressed that according to Athens' view, "a strong Greek-Russian relation could alter the image of the region and Europe."

Greek cabinet sources had said earlier that during Miller's inital visit the two sides could sign an initial memorandum of understanding on a "road map" for the construction of the pipeline.

Miller's visit to the Greek capital comes a few days after Tsipras' visit to Moscow. During talks there with Russian President Vladimir Putin, Tsipras had openly expressed Greece's interest in participating in the project.

According to media reports citing Greek government sources, the two parties were due to sign a deal under which Russia would pay 3-5 billion euros in advance of future gas transit fees to Greece at a time when the debt-laden country was running out of cash this spring without aid from its international lenders and default scenarios increased. However, the Kremlin dismissed the reports during the weekend.

On Tuesday neither side verified the scenario. Analysts have noted that an advance payment would be a bold move for Moscow. The project needs the approval of EU regulators to go ahead and if everything runs smoothly, it was expected to come into service in four years under the best case scenario.

The investment for the construction of the Greek section of the pipeline was estimated at 2 billion euros (about 2.16 billion U.S. dollars), according to the Greek energy ministry, and the project would create about 2,000 job positions in a country where one out of four Greeks was jobless.

Athens also stressed the major contribution of the scheme on the strengthening of Greece's geopolitical standing and the supply safety for the Greek market.

During Tuesday's talks the Greek political leadership and Miller also discussed the participation of Russian companies in the hydrocarbons research in Greece as well as possible reductions on the gas prices Athens pays under an existing contract between DEPA (Greek Natural Gas Company) and Gazprom, according to the Greek Energy ministry.