The Johnnie Walker whisky maker, which holds 28.8% of United Spirits and already has management control, has offered to buy 38 million shares at 3030 rupees (£30) each, compared to 1440 rupees in its initial failed purchase attempt last year. The offer is also at a premium of 18.5% to United Spirits' previous closing price.
Diageo's shares fell 7.00p or 0.37% to 1910p on the news.
The company, which has its headquarters in London, has already spent £728 million building a 28.8% holding in Diageo, much of it purchased from tycoon Vijay Mallya, with additional shares picked up in the market last year.
But Diageo's initial offer to buy another 26% of United Spirits from investors failed last year as its share price soared well above the offer price.
If successful, Diageo, the world's largest spirits maker, will own 54.8% of India's largest spirits maker, guaranteeing majority control of the company.
Currently Diageo has effective control of United Spirits because United Breweries and Mr Mallya, who relinquished control after running into financial difficulties, have agreed to vote with Diageo for four years.
Diageo, which makes Bell's whisky, is currently seeking a buyer for much of United Spirits' whisky arm Whyte & Mackay after competition officials decided they overlap too much in the UK.
If fully subscribed, the offer would be at a 38 times multiple of United Spirits' earnings before interest, taxes, depreciation and amortisation for the year ended March 2013.
Analysts at broker Raymond James said if the deal comes off it "could ultimately be positive news" by boosting Diageo's presence in the fast-growing Indian market.
"United Spirits' strong positions and distribution network would be good leverage for Diageo's spirits brands. However, the price paid for USL is expensive," the broker added.
Andrea Pistacchi, analyst at Citigroup said the price looked high.
But she added: "In our view Diageo is doing the right thing, given the very significant long-term upside for the Indian spirits market and the opportunity, we believe, to significantly raise United Spirits' margins over time."
Diageo remains tied up in legal cases against creditors of United Breweries and United Spirits Benefit Trust from whom it bought shares.
India is the world's largest whisky market. Currently much of this is locally-produced spirit.