For an audience in India, the prime minister is linking his diplomatic reception abroad, and himself, to the country’s growing importance on the world stage.His grip on the levers of national power secure, his hold on India’s domestic imagination cemented, Prime Minister Narendra Modi has increasingly turned to advancing himself on a new horizon: the global stage.With a packed diplomatic calendar that includes India’s hosting of the Group of 20 summit later this year, Mr. Modi is building an image going into his re-election campaign as a leader who can win respect and investment for his vast nation. The state visit accorded to Mr. Modi in Washington, which ends on Friday, is perhaps the biggest prize yet in that quest.“It’s not just about a fairer bargain abroad,” said Ashok Malik, a former government adviser who is the India chair at the Asia Group, a consulting firm. “It’s also that ‘my investments in key foreign policy relations are actually helping to build the Indian economy and therefore create opportunities for Indians at home and strengthen India overall.’”At home, Mr. Modi’s Hindu nationalist party has continued to sideline institutions that were once important checks on the government. It has persisted in its vilification of the country’s 200 million Muslims, even as Mr. Modi used an exceedingly rare news conference in Washington to claim that there was no discrimination against anyone in India.But abroad, world leaders eager to court an ascendant India have offered little pushback. And often, they have given Mr. Modi invaluable fodder for an information campaign that shapes perceptions of him among many Indian voters who are ecstatic to see their country’s importance affirmed.Eid-al Fitr prayers in Chennai, India, in April. Mr. Modi used a news conference in Washington to claim that there was no discrimination against anyone in India, including the country’s huge Muslim minority.Idrees Mohammed/EPA, via ShutterstockWhen Mr. Modi traveled to Australia last month, Prime Minister Anthony Albanese referred to him as “the boss” in front of an arena in Sydney packed with about 20,000 people. Mr. Modi then returned to New Delhi to a large crowd gathered for his welcome at 6 in the morning, telling supporters that the grand welcome for him abroad was about India, not him.On Friday, as Mr. Modi was wrapping up his meetings in the United States before arriving in Egypt for another grand greeting, his political party and the large sections of the broadcast media friendly to him reveled in the reception he had gotten from President Biden and other American leaders.The red carpet in Washington played perfectly into one of Mr. Modi’s talents: He can build a media campaign out of virtually anything, projecting himself as the only leader who can expand India’s economy and usher a nation coming into its own to new heights.While opposition leaders back home were holding their largest gathering yet, hoping to find a formula for uniting to challenge the prime minister in elections early next year, Mr. Modi was reaching for the world.Social media was flooded with montage videos, set to regal background music, of Mr. Modi making a grand entrance into the House of Representatives for his address to a joint session of Congress. The speech, after which several lawmakers sought Mr. Modi’s autograph, made him one of only a very small number of world leaders to have addressed that body twice.Another video online kept count of the number of times Mr. Modi received applause or standing ovations during his speech. A third cut to dramatic images of Mr. Modi contrasting him with the dynastic leaders who came before him, advancing a constant narrative that he represents a subversion of the old elite that long ruled India.“History tells us that powerful people come from powerful places. History was wrong,” a deep voice intones in the video. “Powerful people make places powerful.”Congress offers a standing ovation for Mr. Modi’s speech on Capitol Hill on Thursday.T.J. Kirkpatrick for The New York TimesMr. Modi’s next major opportunity to appear as a global statesman will come in September when India welcomes the Group of 20 leaders, a summit meeting he has framed to his support base as his bringing the world to India.His government has turned promotion for the meeting into a roadshow, hosting hundreds of G20 events, so many that foreign diplomats in New Delhi quietly complain about travel fatigue. Cities and towns across India are decked out with billboards bearing the G20 logo — which cleverly incorporates the lotus, a symbol both of India and his Bharatiya Janata Party — and pictures of Mr. Modi.In promoting the G20 presidency, Mr. Modi has taken to frequently describing India, the world’s most populous nation, as the “mother of democracy.” Abroad, however, he has pursued a transactional brand of diplomacy built not on practicing democratic values, but on what best serves Indian economic and security interests, and what elevates India in the world.The image of “a rising India, a new India being seen more seriously abroad” helps Mr. Modi politically, Mr. Malik said. But Mr. Modi is also investing heavily in U.S. relations with an eye toward how they could help an Indian economy that is struggling to create enough jobs for its huge young population and that must put up a fight against an aggressive China next door.“Addressing China is not just about soldiers and weapons at the border, it’s also about building economic alternatives to what China offers,” Mr. Malik said.Supporters of Mr. Modi’s Bharatiya Janata Party cheer during a rally in Bengaluru, India, last month.Manjunath Kiran/Agence France-Presse — Getty ImagesThe list of agreements between the United States and India, announced at the end of a bilateral meeting at the White House, was long, covering defense, space and a wide range of technological cooperation.Defense cooperation, in particular — including deals on Indian manufacturing of General Electric jet engines and purchasing Predator military drones — received a major boost after what had been a history of reluctance and bureaucratic hurdles on both sides. Dr. Tara Kartha, a former senior official in India’s security council who dealt with U.S. on defense, said the agreement on aircraft engines was “an affirmation of trust” that would help the military partnership beyond the smaller steps of the past two decades.“Each country is trying to get past its bureaucratic constrains,” she said. “Until the bureaucracy can catch up, there will be frustrations.”Among ordinary Indians on the streets of New Delhi, opinions of Mr. Modi’s diplomatic efforts were divided.Vijay Yadav, a 26-year-old taxi driver, said Mr. Modi’s outreach abroad could not cover for how India’s economy was struggling to create enough jobs.“I saw on Instagram a news feed which was constantly touting Mr. Modi’s trip to America as if no other Indian leader had been there before,” he said. “Firstly, he must get down to solving the problems of his own countrymen before he goes abroad to project himself as a hero.”Nidhi Garg, 41, who has inherited a vegetable and fruit shop from her father, said her heart swelled each time she saw Mr. Modi representing India abroad.“Today, wherever you see, the name of our nation is being taken,” she said. “The first thing that comes to anyone’s mind when they mention the word India, they immediately connect it to Prime Minister Modi.”Suhasini Raj More