(CNN) The reincarnation of the Dalai Lama must "comply with Chinese laws," the Chinese Communist Party government has said as the Tibetan spiritual leader recovers in hospital from a chest infection.

Asked about the 83-year-old Buddhist monk's hospitalization on Wednesday, Chinese Foreign Ministry spokesman Lu Kang said Beijing wasn't aware of the physical condition of the 14th Dalai Lama. But he added that there are "clear rules" regarding the reincarnation of "the living Buddha."

"Reincarnation of living Buddhas, including the Dalai Lama, must comply with Chinese laws and regulations and follow religious rituals and historical conventions," Lu said, adding that China respected religious freedom for all its citizens.

The Dalai Lama has lived in India since his self-imposed exile from Tibet in 1959 following the arrival of Chinese troops in the region, which Beijing claims has always been part of China.

Since then, he has become an international celebrity, winning a Nobel Peace prize and feted by some of the world's top leaders. He has also remained a perpetual thorn in the side of the Chinese government.

The Dalai Lama's private secretary Tenzin Taklha said Tuesday the aging monk had been hospitalized with a chest infection after returning to his home in Dharamsala, India, following a meeting in New Delhi.

On Thursday, Taklha said he would be released soon. "He had a chest infection and as suggested by doctors, he took some antibiotics. He is much better now," he said.

But the spiritual leader's illness has once again raised questions over what will happen to Tibetans and their religion when the Dalai Lama dies.

A Tibetan exile activist is detained by Indian police during a protest to commemorate the anniversary of the 1959 Tibetan uprising against Chinese rule, near the Chinese embassy in New Delhi on March 12, 2019.

Last Dalai Lama?

It isn't completely clear whether the Dalai Lama will allow himself to be reincarnated after he dies. The Tibetan spiritual leader has hinted in recent years that he might be the last person to hold the title.

Previously, the title of Dalai Lama, the highest-ranking leader in Tibetan Buddhism, was bestowed on the reincarnation of a line of revered religious teachers, whose identity was chosen by their senior monks.

The 14th Dalai Lama was enthroned when he was four years old after being discovered by a delegation of monks.

Tibetan reincarnation expert Ruth Gamble, at La Trobe University's China Studies Research Center, said there was no requirement for the next Dalai Lama to be born in Tibet.

In a statement released by the spiritual leader in 2011, the Dalai Lama said it was inappropriate for the Chinese government to supervise his reincarnation.

"They say they are waiting for my death and will recognize a 15th Dalai Lama of their choice. It is clear from their recent rules and regulations and subsequent declarations that they have a detailed strategy to deceive Tibetans," he said.

The leader of Tibetan Buddhism said in his statement he would consult with his fellow monks when he was "about 90" on whether the institution of Dalai Lama should continue.

China is an officially atheist state. While the Communist government promises religious freedom to all citizens, there have been worrying signs of a growing crackdown on religion in the past decade.

In the western region of Xinjiang, as many as two million Muslim-majority Uyghurs have been placed in detention centers as part of a policy to eradicate their cultural and religious practices, according to the US state department.

In 2018, authorities tore down dozens of predominantly Protestant Christian churches through the country after ruling that they were built or run "illegally."

Reincarnation subject to approval

The Dalai Lama's fears of interference by Beijing in the reincarnation process are not without precedent.

In the 1990s, a process to find the reincarnation of the 11th Panchen Lama, another important religious leader in Tibetan Buddhism, ended in division and controversy after the Dalai Lama's chosen candidate disappeared and a successor selected by the Chinese government was put in his place.

But Gamble said the Dalai Lama would be under heavy social pressure to reincarnate and, in the end, it might not be up to him anyway.

"In some ways, it's not really his choice. If people go looking for him, they'll find him," she said. The most likely outcome was for two Dalai Lamas to emerge after the 14th holder of the title passes away, Gamble said -- one picked by the Tibetans-in-exile and one selected by Beijing.

Although he no longer calls for Tibetan independence, the Dalai Lama has continued to demand cultural autonomy for Tibet. China calls him a traitor and "a wolf in monk's robes."

He has also remained a point of tension between India and China. Nearly 100,000 Tibetan refugees live in India after fleeing China in 1959.

The Dalai Lama has faded from the spotlight in recent years. In 2018, he announced that he would be cutting back his international travel, citing age and exhaustion.

Asked in a recent interview with Reuters what might happen after his death, the Dalai Lama anticipated a possible attempt by Beijing to foist a successor on Tibetan Buddhists.

In the interview, the 1989 Nobel Peace Prize laureate said: "In future, in case you see two Dalai Lamas come, one from here, in a free country, one is chosen by Chinese, and then nobody will trust, nobody will respect (the one chosen by China). So that's an additional problem for the Chinese. It's possible, it can happen."