The Dalai Lama has cut back on his global engagements and has not met a world leader since 2016
"His Holiness is doing much better, but he is still undergoing treatment at a hospital and we hope in few days he will be discharged," Tenzin Taklha, the Dalai Lama's personal spokesman, told AFP.
Another aide told AFP the 83-year-old Buddhist monk flew to the Indian capital 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," said Ngodup Tsering, the Dalai Lama's representative in the United States.
"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.
A spokeswoman for Max hospital in Delhi said they would not comment on the condition of the Dalai Lama's health due to patient confidentiality.
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.