NEW DELHI » Ever since India’s prime minister, Narendra Modi, visited President Barack Obama in the fall, the word in New Delhi has been that the two men — one a former Hindu activist, the other a former law professor — had "chemistry."

Obama broke the ice by leaving his White House staff behind to give Modi a personal 15-minute tour of the Martin Luther King Jr. Memorial. Soon after, Modi decided to invite Obama to Republic Day celebrations this month, becoming the first Indian leader to choose an American as his guest for the event.

It is hard to say who was more taken aback when Obama said yes: the Americans or the Indians. He is scheduled to arrive in New Delhi on Sunday.

The emerging friendship between the two leaders was not foreordained. Modi came into office with a formidable piece of baggage, having been blacklisted by the U.S. government for nearly a decade over his handling of religious riots in Gujarat, the state he then led. U.S. diplomats’ efforts to mend fences were late and awkward, and Modi is known to hold a grudge.

Beneath the surface of the two leaders’ personal relationship are the shifting tectonic plates of geopolitics. With the expansion of Chinese power into the Indian Ocean, U.S. and Indian interests in the region are gradually converging. It is difficult to say which government was more quietly gratified this month when Sri Lanka’s Beijing-aligned president lost his re-election bid, making it less likely that the island off India’s coast would eventually provide a foothold for Chinese military expansion.

And aides to Modi say the decadelong discussion of Modi’s human rights record concealed an important fact: He is, compared with nearly all of the Indian leaders who preceded him, quite pro-American.

"He was always very canny in recognizing that the United States was important for his own ambitions, and for Indian ambitions," said Ashley Tellis, a senior associate with the Carnegie Endowment for International Peace and author of a new report on the two countries’ relationship. "What was missing was that connective tissue which takes what he knew in his head and translates it into action."

The meeting between the two leaders in Washington, he said, provided that emotional turning point.

This week has brought a marathon of last-minute negotiations, mainly over issues that the United States and India have been grappling with for years.

But Modi has styled himself as a detonator of roadblocks, and some headway may be made this time. A central obstacle is the sweeping liability law passed by the Indian Parliament in 2010 that froze plans for American corporations to construct nuclear power plants in India. Negotiators are also trying to finalize major defense purchases and to close gaps on exports of Indian pharmaceuticals, some of which the United States bans over patent disputes and safety concerns.

U.S. officials, meanwhile, have pressed for India to follow China’s lead and agree to an ambitious target to limit carbon emissions. This week, they played down expectations for a breakthrough, saying they were at an earlier stage with Indian officials than they were with Chinese officials before striking a deal last year with Beijing. But they said the potential seemed to make another trip to India worthwhile, making Obama the first U.S. president to visit twice during his tenure.

"Our hope is that the chemistry between the leaders and the personal relationship can lead to positive outcomes for our country," said Benjamin J. Rhodes, the president’s deputy national security adviser. "And so it’s worth the investment in the relationship with the country, the leader and the people of India."

Famously reserved, Obama does not forge close relationships with other world leaders easily. But Modi has been an exception, aides said, as the two leaders found some shared experiences.

"Just the humble origins from which both of them came from and the opportunities presented to both of them" created a "certain space in which the two leaders were able to engage in these conversations," said Philip Reiner, Obama’s top adviser on South Asia.

When they first met, U.S. officials said, they compared notes on their paths to power, both having won office after campaigns that innovated with new technology. Each of them was seen as ambitious, raising expectations yet struggling to meet public demands for results.

They now stand at very different points, one man confronting the question of how he will stand in history and the other enjoying a glow of international celebrity after years of harsh criticism from the West. Modi, in particular, has given careful thought to the symbolic takeaway of the visit for each leader.

"Go for the big guy himself, and his international rehabilitation is complete," said Ashok Malik, a columnist who advised Modi’s campaign. "What does Obama get out of it? He needs a legacy like nobody’s business."

Since last February, when the U.S. ambassador to India, Nancy Jo Powell, ended America’s nine-year period of not meeting with Modi and held a chilly meeting with him, using a Hindi translator, a series of developments has warmed the atmosphere on both sides.

Powell resigned ahead of schedule. A frustrating trade dispute was swiftly resolved. Modi appointed two senior advisers to his government who had been living in the United States for years. India’s Ministry of External Affairs has distanced itself from a diplomat, Devyani Khobragade, who was arrested in New York last year over her treatment of her maid, providing a rallying cry for anti-American sentiment in India. Indian security officials were delighted at the news that the FBI had opened an investigation into a former U.S. diplomat, Robin L. Raphel, whom they long accused of influencing American policy in Pakistan’s favor.

M.J. Akbar, a spokesman for the Bharatiya Janata Party of Modi, said those steps, some seemingly minor, were part of a larger effort to remove obstacles to better relations.

"Jigsaw puzzles also have very small pieces," he said.

One reason for a closer embrace of Washington by New Delhi is that the members of the new political elite around Modi have far deeper ties to the United States than their predecessors, from the left-leaning Indian National Congress party, which had dominated the country’s politics for 60 years.

Many of Modi’s supporters are Gujarati businessmen who have prospered in the United States and preach the successful immigrant’s gospel of free enterprise and self-reliance. In the 1990s, as a campaigner for the Rashtriya Swayamsewak Sangh, a Hindu nationalist organization, Modi spent months traveling in the United States, and he is said to have avidly studied the country.

Average Indians have a positive view of the United States, as the Pew Research Center found in its most recent survey. But that enthusiasm has never penetrated into India’s government — in particular its defense establishment. The roots of this are deep and historical: The United States has sold advanced weaponry to Pakistan and China and, after India conducted nuclear tests, imposed sanctions on India’s military, cutting off supplies of spare parts and the sharing of technology.

That this gap persists will be demonstrated Monday, when Obama is to stand beside Modi at the Republic Day parade for an extensive display of Indian military hardware, much of it supplied by Russia, India’s preferred vendor for decades. He will also be reminded of India’s pressing need for investment in infrastructure, an area where the United States cannot begin to compete with China’s vast, state-controlled reserves of foreign currency.

Indeed, the most important message from next week’s meeting could end up being a more subtle one: that the relationship is turning, as slowly as an oil tanker, toward a closer, more predictable long-term alignment.

Richard M. Rossow, an expert on Indian-American relations at the Center for Strategic and International Studies, said the president’s decision to return to India so soon after meeting Modi was the best indication that the two men had sized each other up and wanted to move forward.

"Are they buddy-buddy?" he added. "That’s for them to tell you about. But more importantly for the president of the United States, he sees a counterpart that will actually try to deliver on things that are promised in those meetings. And so I think that is probably the best way that they can show friendship."

© 2015 The New York Times Company