Earlier in the day he landed in Gujarat, home state of Prime Minister Narendra Modi, who greeted him along with tens of thousands of Indians.
The leaders of the world's two largest democracies will meet on Tuesday. No big deals are expected to be signed.
Mr Trump received a colourful welcome in the northern city of Agra, which included dancers dressed as peacocks and horses.
While Mr Modi was not present, he was greeted by a close ally of his, Yogi Adityanath, the chief minister of Uttar Pradesh state, where Agra is located.
The Trumps then left for the Taj Mahal, a 17th Century marble mausoleum built by Mughal emperor Shah Jahan in memory of his queen, Mumtaz Mahal.
It is perhaps India's most famous monument and is usually part of every visiting dignitary's itinerary.
Earlier, in Gujarat's Ahmedabad city, Mr Trump addressed a huge crowd at the Motera cricket stadium.
"Namaste," he began to thunderous applause, before going on to refer to several Indian icons, from history to cricket to Bollywood.
"India will always hold a very special place in our hearts," he added.
He also had words of praise for Mr Modi: "Everybody loves him but I will tell you this, he is very tough. You are not just the pride of Gujarat, you are living proof that with hard work, Indians can accomplish anything they want."
However, he struggled to pronounce several Indian words - from Ahmedabad, the city where he was speaking, to Swami Vivekananda, an Indian philosopher, greatly admired by Mr Modi. He also called the Vedas - ancient Hindu texts - "Vestas".
He ended his speech by saying: "God bless India, God bless the United States of America - we love you, we love you very much." He spoke after Mr Modi, and the BBC's Rajini Vaidyanathan says crowds began leaving mid-way through the US president's speech.
Modi in the spotlight
Mr Trump's visit comes at an opportune time for Mr Modi, who has been under the spotlight in recent months following controversial decisions by his government.
In December, India passed a contentious new citizenship law granting amnesty to non-Muslim immigrants from three nearby countries. This prompted massive protests across the country, with critics accusing the government of marginalising India's more than 200 million Muslims - a charge the government denies.
But protests are still continuing, including in Delhi, where a policeman was killed on Monday after violence broke out hours ahead of Mr Trump's visit.
Clashes had erupted between groups protesting against the citizenship law, and those in favour of it.
In August, Mr Modi's government revoked the partial autonomy of the disputed territory of Indian-administered Kashmir, sparking protests in the Muslim-majority valley. Mobile phone connections and the internet have only been partially restored, and political leaders there are still under house arrest along with hundreds of others.
The two decisions have sharply polarised India, and have been questioned by leaders abroad.
But Mr Modi put on a grand public reception to welcome Mr Trump. In Gujarat he was greeted with a road show as crowds lined his route to the stadium. It featured performers from across the country, showcasing the arts from different states.
Billboards along the route to the Motera stadium were emblazoned with pictures of the two men and carried slogans such as "two dynamic personalities, one momentous occasion".
Mr Trump entered to the music of Elton John, which he is known to love, playing on the speakers.
The event is being compared to the "Howdy, Modi!" event that Mr Trump and Mr Modi held in Houston last year, which was attended by 50,000 people.
A visit to Gandhi's home
Mr Trump also made a quick stop at the Sabarmati Ashram, where Indian independence leader Mahatma Gandhi, who was born in Gujarat, lived for 13 years.
He and First Lady Melania Trump tried their hand at the charka or spinning wheel, which is used to spin cloth. Gandhi popularised the act as a form of protest against foreign-made cloth during India's struggle for self-rule.