India’s new Prime Minister Narendra Modi received a boisterous greeting outside his New York hotel on Friday. Around 18,000 people are expected to gather in Madison Square Garden to hear Modi deliver an address on Sunday. (Reuters)

Thousands of supporters are expected to throng midtown Manhattan on Sunday to greet India’s new prime minister, Narendra Modi, a reception more befitting a rock star or a pope than a visiting foreign dignitary.

Modi, the leader of India’s Bharatiya Janata Party, will speak to a capacity crowd at Madison Square Garden on Sunday in a show replete with laser lights, holo­graphic images and former Miss America Nina Davuluri as co-host. The event will be broadcast in Times Square and 100 other venues around the country. The Port Authority of New York and New Jersey has added extra trains to accommodate the expected crowds. A red carpet will be unfurled.

The excitement over Modi’s first visit to the United States is a measure of his popularity at home and the high expectations surrounding his five-day trip, where he will speak at the United Nations, meet business leaders and travel to Washington for a summit with President Obama on Monday and Tuesday.

In the days leading up to the visit, officials on both sides have played down the possibility of any headline-grabbing agreements between the two nations. Rather, the trip is an opportunity for Modi to meet one-on-one for the first time with Obama, congressional leaders and business leaders in his new role. And it is an opportunity to jump-start friendlier relations between the two large democracies, which have been tepid in recent years.

In his four-plus months in office, Modi, 64, has worked to consolidate his power base, reached out to Asian neighbors and tried to tackle some of India’s most pernicious social ills, including substandard sanitation and violence against women.

But it is his vision of a new India — modern, efficient and free of the corruption that dogged previous administrations — that has attracted so many supporters in the United States. So many wanted to hear him speak at the Garden that 10,000 signed up for a lottery for the few seats remaining after most of the 18,000 free tickets were distributed to Indian American community groups.

“Whether you like him or not, he is 180 degrees different from the previous administration,” said Anand Shah, a spokesman for the Indian American Community Foundation, one of the organizers of Sunday’s event. “There’s an opportunity for the rest of the world to engage in India in ways they haven’t in the past, and there’s an opportunity for the country to present a vision people can believe in.”

Yet despite his popularity at home and abroad, the back story over Modi’s controversial past lingers.

When Modi arrived at John F. Kennedy Airport on Friday, it was his first step on American soil since the United States denied him a visa in 2005 on the grounds that he violated religious freedoms while chief minister of the state of Gujarat by failing to do enough to stop Hindu-Muslim­ ­riots. He was formally invited to visit the United States by Obama only after his party’s victory in May’s elections.

Modi has said he harbors no ill will toward the United States, but many in India have not forgotten the controversy, including those who think Modi did nothing wrong. This week, Modi was issued a summons to appear before a New York court as part of a lawsuit by an American civil liberties group representing two of the victims of the Gujarat riots, and human rights protests are expected. Both American and Indian officials dismissed the lawsuit as an unnecessary distraction.

“You see, all this excitement is due to the fact that Mr. Modi was denied a legitimate right to have visited America from 2005 onwards,” said Vijay Jolly, the convener of overseas affairs for Modi’s party. “His style of governance — which found favor among the Indian electorate three times in Gujarat — was never accepted globally by the American government. The American system only accepted him after Mr. Modi achieved a full-fledged majority for the BJP.”

Since then, however, the United States has sent a string of high-level emissaries — including Secretary of State John F. Kerry, Secretary of Defense Chuck Hagel and Sen. John McCain (R.-Ariz.) — to establish ties with the new leader.

And the White House has taken care to extend extra courtesies during the visit, including a private dinner with Obama at the White House on Monday night and a working lunch hosted by Kerry and Vice President Biden at the State Department on Tuesday. These meals will be complicated slightly by the fact that Modi, a Hindu, is in the middle of his customary religious fast.

Obama and Modi share reserved personas and similar modest backgrounds — Modi’s father sold tea in a railway station. But their leadership styles diverge, experts say.

“Their differences are probably more acute,” said W.P.S. Sidhu, a senior fellow for foreign policy at the Brookings India Center in New Delhi. “On one hand, here is a leader who is coming in with a huge mandate and absolute control over the lower house of Parliament. He’s very much a man of action. On the other hand, you’ve got a president who is going into a lame duck session, who has had all kinds of tussles and battles in Congress. He’s not a procrastinator, but he ponders a lot.”

Yet Modi needs American support if he is going to move forward with his vision of expanding India’s infrastructure, building “smart” cities and transforming the railway system. To that end, his meetings with big-name corporate leaders — such as Google’s Eric Schmidt and Goldman Sachs’s Lloyd Blankfein — may be more important than the meetings in Washington, observers say.

Modi must convince foreign investors that India, long a difficult place to do business, is on the path to change. Trade between the two countries was $97 billion last year, and overall direct foreign investment has slowed.

This comes after Modi’s administration made some early missteps, in American eyes, by presenting a clunky budget with no sweeping reforms and blocking a World Trade Organization agreement July 31 because of fears it did not protect Indian food subsidies and stockpiles. Citing the WTO issue and other concerns, the Alliance for Fair Trade With India, a prominent trade group, said in a letter to Obama this week that New Delhi’s “troubling policies” send “perplexing and contradictory new signals about India’s role in the global marketplace.”

To counter such concerns, before hopping on the plane this week, Modi launched a splashy “Make in India” campaign to promote foreign investment in the country. He also penned a Wall Street Journal opinion piece that ran Friday. Aimed at the business community, it pledged he would eliminate unnecessary regulations and bureaucracy.

Modi is a pragmatist, Sidhu said, and realizes that in the end, “it’s the U.S. that has the ability to leverage the financial and economic strength that will really facilitate getting India where it needs to go.”