The success of the auction, the first share sale by New Delhi in eight months, is expected to boost prospects for other state asset sales, although the deal was supported by buying from state institutions.
Excluding the latest sale, it has managed just 1.25 billion rupees so far.
Weak market conditions, corruption scandals and wrangling among government officials have delayed several planned offerings.
"The fact that they are pushing this forward is a positive sign," said Sam Mahtani, a London-based fund manager at F&C Asset Management, which owns Indian shares worth $350 million.
"Obviously they do need the funds to tackle the fiscal deficit," he said.
India may end the year with a fiscal deficit of 5.6 percent of gross domestic product, above an official target of 5.3 percent, a top government official said on Thursday.
That would make it tougher for New Delhi to avoid a credit rating downgrade.
The auction of India's third-largest copper producer drew bids for 51.6 million shares, stock exchange data showed, representing 5.6 percent of its share capital.
New Delhi offered 37.01 million shares, or 4 percent of the company, but had the option to sell a further 51.71 million. The government is likely to exercise the overallotment option and allocate all shares for which it received bids, two sources with direct knowledge of the matter said.
The bids had a weighted average price of 156.56 rupees a share, exchange data showed, slightly above the 155 rupees floor price.
The government owns 99.59 percent of Hindustan Copper, and the limited free float had inflated the traded price of the shares. The stock fell about 20 percent, its daily limit, on Friday to 212.95 rupees.
Mumbai-based Angel Broking had advised investors to avoid buying shares in the auction due to a high valuation.
At the floor price, the stock's enterprise value is equivalent to 24.5 times the company's earnings before interest, tax, depreciation and amortisation, compared to five to 10 times at peers Coal India