The Dalai Lama has undergone a check-up at a New Delhi hospital following chest pains, according to an aide who said the Tibetan spiritual leader was in stable condition.

Ngodup Tsering, the 83-year-old Buddhist monk's representative in the United States, told AFP the Dalai Lama flew to New Delhi early Tuesday for a doctor's visit at Max hospital after he experienced a "light cough."

"The doctor said there's nothing to worry about. It's not that serious," Tsering said, without confirming whether the Dalai Lama had been admitted for hospital treatment. "He's taking a few days' rest."

Kangra police superintendent Santosh Patial told The Indian Express that the Dalai Lama, who is based in Dharamshala and has been in permanent exile in India for some 60 years, took a regular morning flight Tuesday and was not airlifted.

"There is nothing to panic," he added.

Although the exiled leader remains a hugely popular speaker, he has cut back on his global engagements and has not met a world leader since 2016 -- while governments have been wary of extending invitations to him for fear of angering Beijing.

The Dalai Lama has sought to pre-empt any attempt by Beijing, which has effectively wiped out any organized opposition to its rule in Tibet, to name his reincarnated successor, even announcing in 2011 that he may be the last in the lineage.

The Tibetan spiritual leader enjoys wide support across the partisan divide in Washington, where a senator raised the issue of his succession at a hearing Tuesday.

Senator Cory Gardner, the Republican who heads the Senate Foreign Relations subcommittee on Asia, said that the United States should follow the Dalai Lama's lead on how to choose his successor.

"Let me be very clear -- the United States Congress will never recognise a Dalai Lama that is selected by the Chinese," Gardner said.

But even India, which offered asylum to the Dalai Lama in 1959 when he made a daring escape across the Himalayas dressed as a soldier, has turned its back, with the government reportedly warning officials against attending events featuring him, citing diplomatic sensitivities.