Earlier on Monday, thousands of people gathered for a mega-rally in his honour, where the President told crowds "America loves India".
Mr Trump was embraced by Prime Minister Narendra Modi after Air Force One touched down in Ahmedabad in western India.
President Trump told crowds "America loves India. America respects India":
Speaking at the Motera Stadium in Prime Minister Modi's hometown, Mr Trump expressed gratitude to the Indian Prime Minister's "spectacular welcome" and to the public for a "stunning display of Indian culture and kindness".
The rally, at the world’s second-largest stadium, heard President Trump announce: "America loves India. America respects India"
He added: "America will always be faithful and loyal friends to the Indian people."
First stop on the Presidential visit was a former home of independence leader Mohandas Gandhi.
Mr Trump donned a prayer shawl and took off his shoes before walking through the humble ashram.
He inspected the loom used by the famed pacifist and looked at statues of monkeys representing Gandhi’s mantra of "See no evil, Hear no evil, Speak no evil".
Mr Trump's foreign visits have typically been light on sightseeing, but this time the President and Mrs Trump also visited the Taj Mahal for a sunset tour.
As Mr Trump walked from the iconic 17th century mausoleum, he told reporters that is was an "incredible place".
The President used to own the Taj Mahal Casino in Atlantic City, New Jersey.
Ahead of the Trumps' visit, the sun-baked city of Ahmedabad had been jostling with activity in preparation with workers cleaning roads, planting flowers and hoisting hundreds of billboards featuring the President and First Lady Melania Trump.
For his arrival, Mr Trump’s motorcade travelled amid cheers from a carefully selected and vetted crowd of Modi loyalists and workers from his Bharatiya Janata Party.
The supporters stood for hours alongside the neatly manicured 14-mile stretch of road to give the president a grand welcome on his way to the Sardar Patel Stadium.
Tens of thousands of police officers were on hand to keep security tight.
A new wall has also been constructed in front of a slum in the city, which critics say was built to hide it from presidential passers-by.
"I hear it’s going to be a big event.
"Some people say the biggest event they’ve ever had in India," Mr Trump said before he left Washington.
"That’s what the Prime Minister told me - this will be the biggest event they’ve ever had."
The visit comes at a crucial moment for Mr Modi, a fellow populist, who has presided over a steep economic downturn and unfulfilled campaign promises about job creation.
Mr Trump will on Tuesday conclude his visit to India with a day in New Delhi, complete with a gala dinner and meetings with Mr Modi over stalled trade talks between the two nations.