"Diversity is basis of our democracy", the prime minister said.
While introducing the United States president, Modi first spoke in English and noted that Trump's name "comes up in nearly every conversation in the world on global politics".
Even as the event is set to begin, Indians in the U.S. have started lining up outside the NRG Football stadium.
"We are challenging ourselves", he said, adding that India today is challenging the mindset that nothing will change ever.
Trump has already made the American economy strong again, Modi said.
"Lauding the Indian-American community, Trump said, "(I am) especially grateful to be joined by over 50,000 incredible members of thriving, prosperous, flourishing, hardworking Indian American community" and four million "amazing Indian Americans who enrich our culture, uphold our values.you are truly proud to be Americans".
This will make Indian companies competitive, he said. "But, he is a master of the Art of the Deal and I am learning a lot from him", he stated.
He invited Trump to India with family. In words that regaled the audience as Modi listened in, Trump said, "We are committed to protecting lives of innocent from rabid Islamic terrorism..."
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"India and the USA also understand that to keep our community safe, we must protect our borders".
Trump inserted a couple of India-specific lines into his stump speech as he addressed the stadium's crowd, estimated at 50,000.
With Trump watching in the front row and listening to the translation, Modi made clear reference to rival Pakistan, which controls part of Kashmir and has sought to rally worldwide attention over the Himalayan territory.
In a video tweeted out by the Prime Minister's office, Modi is seen addressing Cornyn's wife Sandy, and saying, "I would like to say sorry because today is your birthday and your great life partner is with me so naturally, you must be jealous today".
Later, it completely merged into the United States as the 28th state of the nation.
Modi said he met Trump a few times and every time he has been warm, friendly, accessibly, energetic and full of wit. Border Security is vital to India.
President Trump has stated several times that he is willing to "mediate" on the issue of Kashmir between New Delhi and Islamabad, but Modi has reiterated India's policy that the dispute doesn't warrant third-party intervention.
Trump and Modi both spoke at the event, championing the economic relationship between the two countries and the jobs created in the Trump administration.
Once Modi ended his speech at 10 minutes past midnight India time, he went up to Trump and both the leaders walked out of the stadium, holding their hands for a long time.