Sechin, who heads Rosneft, Russia's biggest oil company, led a delegation of about two-dozen officials to meet Oil Secretary Saurabh Chandra seeking to expand ties with New Delhi.
"India is a very important country for Russia. We have a very efficiently run project with ONGC...Now we want to expand our cooperation," Sechin told PTI after the meeting.
The Russian state oil major offered Oil and Natural Gas Corp (ONGC) a stake in nine offshore oil and gas blocks in the Barents Sea and one in the Black Sea.
Moscow is courting India to counter moves by the US and Europe to isolate it for annexing Crimea from Ukraine. Sechin was in Tokyo last week to broaden ties with Japan.
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India does not have a firm contract to import crude oil from Russia. It gets a small volumes once in a while from ONGC's Sakhalin-1 project in Far East Russia.
Indian officials said logistics need to be worked out to import oil from Rosneft's fields.
Of the blocks offered in the Barents Sea, OVL found five were not lucrative. Of the remaining four, it would like to participate in two. It will decide on the other two once Rosneft makes available data by June.
Rosneft had previously offered ONGC a stake in the Magadan 2 and Magadan 3 exploration blocks in the northern part of the Sea of Okhotsk, which the Indian firm is studying.