Sinha's comments came a day after the International Monetary Fund predicted Asia's third-largest economy would become the fastest growing major economy in the world, outpacing China.
The rupee has been convertible on the current account since 1994, meaning it can be changed freely into foreign currency for purposes like trade-related expenses.
But it cannot be converted freely for activities such as acquiring overseas assets.
Fuller convertibility is expected to facilitate rapid growth through higher investment and improve efficiency in the financial sector through greater competition.
"If we have to be among the top three-four economies in the world, we have to make it possible for our capital markets to be broader and deeper, and for that to happen capital account convertibility also becomes important," Sinha said, without specifying any time frame.
Last week, Reserve Bank of India chief Raghuram Rajan expressed hope that the rupee would become fully convertible in a "short number of years".
Analysts say India's inflation, interest rates, and trade and financial system would have to be globally competitive before it allows free movement of capital in and out of the local currency.
In mid-2013, the central bank was forced to resort to capital controls to stabilise a fast sliding rupee after foreign funds started pulling out of the country in the wake of speculation over when the US Federal Reserve would taper its massive bond buying programme.
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