Thatcher, the then British prime minister, sent the note to her Indian counterpart Gandhi, saying Britain supported India's unity in the face of demands for a separate Sikh homeland and that police were investigating threats against the safety of Indian diplomats here, the Guardian reported.
In what appears to be the first letter to Gandhi after the operation, sent on June 30, 1984, Thatcher wrote: "These have been anxious weeks for you, involving difficult decisions. I have followed closely your efforts to restore calm there, and I very much hope that the 'healing touch' for which you have called will open the way to a peaceful and prosperous future in that troubled region."
The letter, seen by the Guardian, will form part of an investigation launched by Cabinet Secretary Jeremy Heywood on Prime Minister David Cameron's orders to determine the British government's involvement in the operation.
Thatcher's note, in response to two letters sent by Gandhi on June 9 and 14, appears to show that the Indian prime minister had expressed worries that Sikh "extremists" could use Britain as a base, the report said.
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In an apparent reference to death threats against Gandhi which had been reported in the British media, the UK prime minister who died last year wrote: "We have made sure the police are aware of these statements and they are investigating them."
Thatcher also reassured Gandhi that British police were "devoting considerable resources" to safeguarding Indian government personnel in Britain, the report said.
Labour MP Tom Watson and Pat McFadden, in the House of Commons, had raised the issue of Britain's role in the operation that left over 1,000 people dead, demanding full disclosure.