OVL's biggest overseas acquisition so far is contingent upon approval from Kremlin.
Petroleum Minister Murli Deora met Medvedev on the sidelines of the Shanghai Cooperation Organisation summit in Dushanbe and sought his support of the deal, officials present at the meeting said.
"The Russian President promised to support OVL and even called his energy advisor to issue instructions," one of the officials said.
When contacted Deora said, "We had very good meeting with the President and I am very happy at the outcome." He refused to elaborate.
If Kremlin approves, Imperial would be biggest overseas acquisition for OVL, the overseas arm of Oil and Natural Gas Corp (ONGC).
It had paid USD 1.7 billion to buy a stake in Exxon Mobil Corp's Sakhalin-I field in Russia and USD 785 million for a stake in the Greater Nile project in Sudan, both in 2003.
The board of Imperial had earlier this week recommended OVL's 1,250 pence a share bid but it has to win approval of Russian authorities to materialise.
The Kremlin may want the Indian firm to sell part of the Imperial stake to a Russian state oil group such as Rosneft, which OVL is open doing so.
Kremlin has during recent years increased its control on the Russian oil sector.
State-backed firms managed majority stakes in big, formerly privatised energy assets. In 2006, Sinopec bought Udmurtneft, a 120,000 barrels per day crude production unit from BP's Russian unit TNK-BP for about USD 3.5 billion but later sold a 51 per cent stake to Rosneft.
Officials said they were hopeful of Russian support for OVL which must happen quickly as China Petroleum or Sinopec may make a counter bid.
"We have good relations with the Russian government and we hope we will get clearance soon," OVL Managing Director R S Butola had stated on Tuesday.
Imperial Energy will give OVL, which already has a 20 per cent stake in Sakhalin-1 project in Far East Russia, access to Siberia, an area believed to hold huge hydrocarbon deposits.
Imperial, a relatively small British oil and gas company based in Leeds in the UK, has oil producing blocks in Tomsk region of the western Siberia in Russia and Kastanai in north-central Kazakhstan.
The bid values Imperial's 920 million barrels recoverable oil reserves at around USD 2.77 per barrel.
Imperial produced 10,000 barrels of oil equivalent per day at the end of 2007 but plans to raise this to 25,000 by the end of 2008 and to 80,000 barrels per day (four million tons a year) by the end of 2011.