“I’ve long believed that the relationship between the United States and India will be one of the defining relationships of the 21st century,” Mr. Biden told a crowd gathered on the South Lawn, “two proud nations whose love of freedom secured our independence, bound by the same words in our Constitution, the first three words, ‘we the people.’”

Mr. Modi thanked Mr. Biden for the honor of a state visit and likewise suggested the two nations could tackle international challenges in tandem. “In the post-Covid era, the world order is taking a new shape,” he said through a translator. “In this time period, the friendship between India and the U.S. will be instrumental in enhancing the strength of the whole world.”

The visit is the latest move on the geopolitical chess board as Mr. Biden seeks more allies against increasingly aggressive governments in Moscow and Beijing. India, which remained staunchly nonaligned during the Cold War, has refused to join the American-led coalition aiding Ukraine in its war against invading Russian forces. And while it shares a certain enmity for China, it has not fully subscribed to Washington’s strategy for dealing with the Asian giant.

India, whose population recently surpassed China’s to lead the world, represents perhaps the most important of the so-called Global South nations that Mr. Biden is pursuing, both for its economic potential as well as for its geopolitical position. And Mr. Modi, without directly referring to that in his own remarks at the arrival ceremony, nonetheless alluded to India’s growing power, mentioning its population of 1.4 billion three times in just a few minutes.

To mark their ties, the two leaders planned to announce a long list of initiatives advancing cooperation on telecommunications, semiconductors, artificial intelligence and other areas, according to administration officials. Mr. Modi intended to sign the Artemis Accords, a set of principles governing peaceful exploration of the moon, Mars and other celestial bodies, and the two will announce a joint mission to the International Space Station in 2024.

Among the most concrete agreements to be announced, officials said, will be a deal between General Electric and the state-owned Hindustan Aeronautics Limited to manufacture in India F414 engines used to power the Boeing F/A-18E/F Super Hornet. The two sides will also announce that India will proceed with a long-stalled $3 billion purchase of MQ-9B Predator drones from General Atomics.

The military hardware sales may help continue to wean India off Russian arms suppliers, but otherwise officials previewing the visit offered no indications that Mr. Modi would move closer to backing Ukraine in the war, nor were there any concrete examples of increased cooperation to counter China’s assertive moves in the Indo-Pacific region.

Biden administration officials suggested the meeting was just one step in an evolution of India’s stance on the Ukraine war, part of what they characterized as “bending the arc of India’s engagement,” so New Delhi can be helpful in encouraging diplomacy when the time for negotiations eventually arrives.

But in cultivating Mr. Modi, who before becoming prime minister was denied a U.S. visa because of his role in a deadly religious riot in his home state, it was clear that Mr. Biden was taking a soft approach to backsliding on democracy in India, where the government has cracked down on dissent and hounded opponents. In his welcome remarks, Mr. Biden described the two countries as fellow democracies committed to universal values without directly mentioning the increasing suppression of minority groups and opposition voices in India.

“Equity under the law, freedom of expression, religious pluralism, diversity of our people — these core principles have endured and evolved even as they have faced challenges throughout each of our nations’ histories, and will fuel our strength, depth and future,” Mr. Biden said.

Officials said the president will raise human rights issues during his later private meeting with Mr. Modi, but in briefing reporters ahead of the visit they used the word “respectful” more than once to characterize Mr. Biden’s approach.

They considered it a victory that the administration had persuaded Mr. Modi, who famously refuses to hold news conferences, to meet with reporters alongside Mr. Biden, as most major world leaders do when they visit the White House. Even then, the White House avoided using the term “news conference”; its public schedule said the leaders would “take questions from the press” in the East Room.

Several liberal Democrats in Congress plan to boycott Mr. Modi’s speech to a joint session later on Thursday. “A joint address is among the most prestigious invitations and honors the United States Congress can extend,” Representative Alexandria Ocasio-Cortez of New York wrote on Twitter. “We should not do so for individuals with deeply troubling human rights records.”

The scene on the South Lawn in the morning underscored the rising role of Indian Americans in the United States as a crowd of thousands gathered on a gloomy, overcast day to cheer the prime minister’s visit and chant, “Modi, Modi!”

Mr. Biden pointed to the prevalence of Indian Americans in prominent positions. “We see it here at the White House where proud Americans of Indian heritage serve our country every day — including our vice president of the United States, Kamala Harris,” he said, turning to Ms. Harris standing off to the side.

Ms. Harris’s mother emigrated from India to the United States as a teenager and Mr. Biden cited the story of “a family like so many of ours in our nation that speaks to the thousands of stories of determination, courage and hope.”

The state dinner, only the third of Mr. Biden’s presidency, will be held on the South Lawn in a pavilion draped in green with saffron-colored flowers at every table, the colors of the Indian flag. Lotus blooms, an important symbol in India, will be incorporated throughout the décor. Images of the bald eagle and the peacock, the national birds of the two countries, will be displayed as the backdrop when the leaders offer their traditional toasts.

The menu will be vegetarian, in accordance with Mr. Modi’s diet, with an optional fish entree. The first course will be a marinated millet and grilled corn kernel salad with compressed watermelon and avocado sauce, followed by a main course of stuffed portobello mushrooms and creamy saffron-infused risotto. A sumac-roasted sea bass will be available upon request. A rose and cardamom-infused strawberry shortcake will be served for dessert.

Joshua Bell, the Grammy-winning violinist, will perform, as will Penn Masala, a South Asian a cappella group founded by students at the University of Pennsylvania, and the U.S. Marine Band chamber orchestra.