The London-listed group, headed by Anil Agarwal, has been in talks with the Indian government for more than two years to acquire the remaining stakes in Bharat Aluminium Company (Balco) and Hindustan Zinc.
Currently, Vedanta Resources has 64.9 per cent stake in Hindustan Zinc and 51 per cent in Balco.
The government currently holds 29.5 per cent stake in Hindustan Zinc and 49 per cent in Balco.
The entity would seek shareholders' approval for the revised proposal during their meeting on October 30 in London.
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In January 2012, Vedanta had offered to acquire government's stake in Hindustan Zinc and Balco USD 2.938 billion and USD 338 million, respectively.
According to Vedanta, the current offer price is assumed on the spot exchange for Indian rupee of 62.1383 against the US dollar. The rate is as on October 13.
Till date, neither offer has been accepted by the government, which may determine to retain its interests or to seek to sell its interests to one or more third parties, the letter dated October 14 said.
"Accordingly, there is no certainty that the group will acquire all or any part of the Government of India's interests in Hindustan Zinc and/or Balco.
"If the entirety of the Government of India's interests are acquired, the group's interests in Hindustan Zinc and Balco would increase to 94.4 per cent and 100 per cent, respectively, and Vedanta's economic interests in Hindustan Zinc and Balco would increase to 55 per cent and 58.3 per cent, respectively," it noted.