In a filing to the Bombay Stock Exchange, HOEC said as per the revised schedule the open offer would open on July 2 and close on July 21.
Earlier, the firm had announced that the open offer would begin on June 11 and close on June 30.
In April, Eni had offered to buy an additional 20 per cent stake, over 2.61 crore shares, in HOEC for Rs 144.2 a share.
The open offer for the 20 per cent stake came after Eni SpA bought UK crude producer Burren Energy Plc, which owns 27.17 per cent in HOEC. The transaction led to an indirect purchase of 27.17 per cent interest in HOEC.
As per the country's takeover rules, Eni Holding was to make an open offer for not less than 20 per cent of HOEC's outstanding shares. The aggregate consideration payable under the offer (assuming full acceptance) is Rs 376.58 crore.
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Last year, Eni bought Burren Energy for $3.6 billion to add production capacity in Africa, the Caspian and India.
The open offer was made by Eni UK Holding Plc along with Burren Energy India Ltd and Burren Shakti Ltd.
Burren Energy is the holding company of Burren Shakti Ltd and Burren Energy India Ltd, which together own 27.12 per cent in HOEC.
N M Rothschild & Sons India is the manager to the offer. Shares of HOEC closed at Rs 130.30, up nearly 10 per cent on the BSE.