The move could boost gold supplies and bring down premiums for the metal in the world's second-biggest consumer after China.
India's central bank has allowed gold imports by HDFC Bank , Axis Bank, Kotak Mahindra Bank, IndusInd Bank and Yes Bank, officials at the respective banks told Reuters.
Two industry sources confirmed the names of the banks. They and the bank officials did not want to be named as they are not authorised to speak to media.
India enforced the so-called 80/20 rule in July, making it mandatory to export a fifth of all gold imports. Under that rule, only six banks and three state-run trading agencies that had facilitated export of gold or jewellery in the past three years were allowed to import. The six banks were mostly state-run lenders.
The Reserve Bank of India - the central bank - has now permitted gold imports within prescribed limits by the private banks even though they had not facilitated any exports of metal or jewellery in the past three years.
"They have decided upon limits on quantities depending upon the number of (current) customers you have for exports," said Shekhar Bhandari, executive vice-president of Kotak Mahindra Bank.
The Reserve Bank of India did not immediately respond to a request for comment.
The move to allow more banks to import gold may raise shipments to about 40 tonnes per month from more than 20 in February, industry officials said. India used to ship in as much 70 tonnes per month, the biggest import after oil that had pushed the current account deficit (CAD) to a record high in the year ended March 2013.
"Supplies will be smooth from now and I think premiums will come down," said Haresh Soni, chairman of the All India Gems and Jewellery Trade Federation. "This looks like just a beginning to the further easing of 80/20 rule."
NEW GOVERNMENT, NEW RULES
India used to be the No. 1 buyer of gold before the levy of a record 10 percent import tax in stages and other restrictions led to a sharp cut. Premiums hit a record of $160 an ounce in December, triggering smuggling and forcing industry officials to call for a repeal of the curbs.
Further major relaxations of the curbs are likely only after a new government is formed around June, officials involved with policymaking said.
Finance Minister P. Chidambaram said earlier this month the gold import duty could be revisited only after the final CAD numbers are out.
The CAD, final figures for which are expected to come in the first week of June, is likely to fall to less than $40 billion for the fiscal year ending March 31 from its record $88 billion in the previous year.
By that time it will also be clear who will form the government, after India's general elections that start in April. The main opposition Bharatiya Janata Party - the favourite to win the polls - has already spoken against the gold import restrictions.
Its prime ministerial candidate Narendra Modi has said that any action on gold should look at the interests of the public and traders, not just economics and policy.
A senior policy official aware of the deliberations said the government and the central bank wanted to gradually remove the curbs as falling gold prices are expected to cut the CAD by $10-$12 billion.
"We don't believe in artificial kind of compression of current account deficit," the official said. "Since it was an extraordinary kind of situation and it was a policy option available, we tried that."
The official estimates India's gold imports this fiscal year to be around 800-850 tonnes, lower than last year's 950 tonnes.