One week after joining President Donald Trump on a state visit to Beijing, Rubio -- visiting both Asian powers for the first time -- flew to New Delhi and met Modi for more than an hour, inviting the premier to visit the White House soon.

"The world's oldest democracy in the United States and the world's largest democracy here in India are natural partners now and in the future," said Rubio, sporting a tuxedo in the searing heat as he entered a gala dinner for business and political leaders at the US ambassador's residence.

Modi said he discussed with Rubio issues related to regional and global peace and security.

"India and the United States will continue to work closely for the global good," he said in a social media post.

Cutting a ribbon earlier at a new US embassy building, Rubio said the US-India relationship lay "at the cornerstone of our approach to the Indo-Pacific".

Such glowing statements were for decades routine between the United States and India.

But Trump has shattered assumptions about US foreign policy and last year took his distance from India, whose leaders avoid the lavish, personal praise that the US president has come to expect from allies.

Trump last year imposed punishing tariffs on India, which were eventually eased, and India was barely mentioned in his administration's national security strategy.

Trump, despite limited concrete announcements in Beijing, spoke of the United States and China as a "G2" -- a formulation resented by US allies who fear being shut out of Washington's dealings with a rising China.

- Unease on visas -

India has also been alarmed by Trump's strident anti-immigrant rhetoric and his crackdown on visas used by tech professionals.

In its latest move, the Trump administration on Friday said applicants for US residency, even when in the United States legally, need to leave to apply, likely tearing apart many immigrant families.

In an interview with India's NDTV news network in New Delhi, Rubio said the move was aimed at addressing a global "migratory crisis" and was "not about India" specifically.

But he acknowledged, "there's going to be some inconvenience".

- Starting with nuns -

Rubio, a devout Catholic, began his four-day, four-city tour by touring the headquarters of Mother Teresa's charity in the eastern city of Kolkata and praying over her tomb.

Wearing a yellow garland over his suit, Rubio, joined by his wife Jeanette, smiled before an assembly of nuns, all clad in the late humanitarian's signature white and blue saris.

"Rubio spoke about aiding the homeless, terminally ill and those afflicted by leprosy," Sister Marie Juan of Missionaries of Charity told reporters after his hour-and-a-half-long visit.

"He was happy to pray, and we were also happy to have him," she said.

While Trump rarely raises human rights, some elements of his base have expressed concerns over the treatment of Christians under the Hindu nationalist Modi, making Rubio's choice of first stop highly symbolic.

Rights groups say there has been a rise in attacks on minority Christians across India, including vandalism of churches, since Modi came to power in 2014.

The government rejects the claims as exaggerated and politically motivated.

Before leaving on Tuesday, Rubio will also take part in a meeting of foreign ministers of the so-called Quad -- Australia, India, Japan and the United States.

China has long been suspicious of the Quad, calling it an attempt to encircle it.

The Iran war has also seen the diplomatic re-emergence of India's traditional adversary Pakistan, which has positioned itself as the key mediator for Washington, with its powerful army chief visiting Tehran.

The United States was a Cold War partner of Pakistan but gradually prioritised relations with India, annoyed by Islamabad's role in Afghanistan.

Trump was ecstatic after Pakistan said he deserved the Nobel Peace Prize over his diplomacy in its short war with India last year.

Modi irritated Trump by not crediting him with ending the war, in which India struck Pakistan following the massacre of mostly Hindu civilians in Indian-administered Kashmir.