The Karmapa - who ranks third behind the Dalai Lama and the Panchen Lama - is at the well-guarded headquarters-in-exile of the Dalai Lama, on the outskirts of Dharamsala.
Defence Minister George Fernandes said the 14-year-old spiritual leader could stay in India while the investigation into his secret flight from Tibet continued.
Mr Fernandes said he could not see why the Karmapa wanting to stay in India for a while should impinge on relations with Beijing.
And India had not received any formal asylum request from the Buddhist leader, he said.
Correspondents said that although the defence minister was one of the few in Delhi to have spoken out about the issue, there were no imminent moves to ask the Karmapa Lama to leave India.
High-ranking monk
The 17th Karmapa Lama is the only senior Tibetan Buddhist leader recognised by both the Dalai Lama and China, and his flight from Tibet is seen as a blow to China's religious policy there.
The Karmapa - who ranks third behind the Dalai Lama and the Panchen Lama - is at the well-guarded headquarters-in-exile of the Dalai Lama, on the outskirts of Dharamsala.
The young lama arrived in India on 5 January after an arduous eight-day journey by car and on foot across the Himalayas.
The Dalai Lama's officials said he fled Chinese pressure on the Buddhist monasteries in Tibet.
China said he had left to collect the black crown and musical instruments associated with his Buddhist lineage.
The 16th Karmapa brought the crown with him when he fled Chinese-ruled Tibet in 1959, and deposited it in his monastery at Rumtek, which is now part of India.
The young lama himself has yet to give his own version of events - and correspondents say he is not likely to until India decides on what terms he might be allowed to stay in the country.
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