ATHENS (Reuters) - Greece's privatisation agency on Monday asked a consortium led by Italy's Snam, which made the highest bid for a 66 percent stake in gas grid operator DESFA, to further improve its offer.

Greece relaunched the sale last year as part of its latest 86 billion euro international bailout, and after a previous 400 million euro (345.6 million pounds) deal with Azerbaijan's SOCAR fell through in 2016.

Athens received two binding bids last month, one from Italy's Snam, Spain's Enagas Internacional (>> Enagas) and Belgium's Fluxys, and the other from a consortium of Spain's Regasificadora del Noroeste, Romania's Transgaz and the European Bank for Reconstruction and Development (EBRD).

Greece asked both bidders to raise their offers and the improved bids, which were not disclosed by the privatisation agency, were unsealed on Monday.

Greece's Energy Minister George Stathakis said in a statement that the amount offered by the Snam-led consortium was higher than that offered by SOCAR in the previous tender, and that the terms had been improved, in favour of the state.

"We expect, in the next hours, the submission of the final bid and the successful completion of the tender," he said.

Stathakis added that the chairman of DESFA's board would be appointed by the state which will also have the right to veto decisions, including DESFA's participation in projects at home and abroad. The new buyer should also implement a 330 million euro investment plan, he said.

Athens is selling a 31 percent stake and Hellenic Petroleum, Greece's biggest oil refiner, 35 percent.

The further improved bid will be assessed by HRADF's board of directors and by Hellenic Petroleum, the privatisation agency said.

Greece, which exits its third bailout in August, aims to conclude the deal this year.

DESFA owns and operates Greece's natural gas network and a liquefied natural gas terminal on an islet off Athens. It is considered a valuable asset as domestic gas consumption rises and Greece seeks to boost its regional energy market presence.

DESFA transports gas from the Greek-Bulgarian and Greek-Turkish borders via a 1,459-km (907-mile) pipeline.

(Reporting by Renee Maltezou and Angeliki Koutantou, editing by David Evans and Alexander Smith)

By Renee Maltezou and Angeliki Koutantou

Stocks treated in this article : Snam, Enagas, Hellenic Petroleum, Fluxys Belgium