"I would like to invite you to India, along with your family. And I hope that you will give me the opportunity to welcome you and host you in India," PM Modi said in his remarks, standing alongside Mr Trump at the White House's Rose Garden.
The two leaders met for the first time as PM Modi was in US on the second leg of his three-nation tour. They held extensive talks during their bilateral meeting. Mr Trump called PM Modi "true friend" and thanked him for visiting the US and the White House, saying their "very productive conversation".
The 66-year-old leader also invited President Trump's daughter to India to lead the US delegation of entrepreneurs to the Global Entrepreneurship Summit in India later this year. "...And I believe she has accepted," Mr Trump said.
Ivanka, an American businesswoman and former fashion model, is also an assistant to her father.
This is PM Modi's fifth visit to the United States, the first after Trump administration took charge of the office. The leaders of the two powerful democracies have talked over phone three times.
PM Modi will now head to Netherlands on his last leg of the trip.
With inputs from PTI and IANS