Cameron asked Cabinet Secretary Jeremy Heywood to conduct the investigation after documents declassified under the 30-year rule suggested a British special forces officer advised the Indians on carrying out the attack.
The premier's spokesman said the investigation will examine two issues -- British action in 1984 and the decision to release such sensitive government papers.
Labour MP Tom Watson and Lord Indarjit Singh had demanded an explanation after documents made public over the New Year indicated that an officer of Britain's Special Air Service was dispatched to help India plan for the raid on the Golden Temple, an operation that left over 1,000 people dead.
"These events led to a tragic loss of life and we understand the very legitimate concerns that these papers will raise. The prime minister has asked the Cabinet Secretary to look into this case urgently and establish the facts," a government spokesman said.
"The PM and the Foreign Secretary were unaware of these papers prior to publication. Any requests today for advice from foreign governments are always evaluated carefully with full ministerial oversight and appropriate legal advice."
The documents being referenced were released by the National Archives in London under the 30-year declassification rule as part of a series over the New Year.
A "top secret and personal" letter, dated February 23, 1984, nearly four months before the raid in Amritsar, and titled "Sikh Community", stated: "The Indian authorities recently sought British advice over a plan to remove Sikh extremists from the GoldenTemple in Amritsar.
"The Foreign Secretary decided to respond favourably to the Indian request and, with the Prime Minister's agreement, an SAD (sic) officer has visited India and drawn up a plan which has been approved by Mrs Gandhi. The Foreign Secretary believes that the Indian Government may put the plan into operation shortly."
Lord Singh, director of the Network of Sikh Organisations in the UK, told PTI: "These documents prove what Sikhs have suspected all along, that plans to invade the Golden Temple went back months even though the Indian government was claiming even weeks before that there were no such plans."
"I have already approached the Indian government through the High Commission of India for the need of an independent international enquiry to establish the exact facts. I will now raise the issue in the House of Lords," he added.
Some of the documents have been reproduced on the "Stop Deportations" blog that focuses on UK's immigration policy, and claim Thatcher sent an SAS official to advise Gandhi on the operation.
Watson, an MP for West Bromwich East, said he had been told there were other documents that had been withheld. "This is not good enough. It is not unreasonable to ask for an explanation about the extent of British military collusion with the government of Indira Gandhi," he said.
He has written to Foreign Secretary William Hague and plans to raise the issue in the House of Commons.
"I think British Sikhs and all those concerned about human rights will want to know exactly the extent of Britain's collusion with this period and this episode and will expect some answers from the Foreign Secretary," he said.
"But trying to hide what we did, not coming clean, I think would be a very grave error and I very much hope that the foreign secretary will...reveal the documents that exist and give us an explanation to the House of Commons and to the country about the role of Britain at that very difficult time for Sikhism and Sikhs."
Five months after Operation Bluestar, Gandhi was assassinated by her Sikh bodyguards in retaliation for the raid on the Golden Temple.
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