In a joint news conference, he said he looked forward to improving the trading relationship between the two countries.
Mr Modi said he and Mr Trump had agreed to improve co-operation on fighting terrorism.
The talks at the White House were the first time the two leaders had met face to face.
"The relationship between India and the United States has never been stronger, never been better," President Trump told the news conference in the White House Rose Garden.
Mr Trump, who regularly posts on Twitter, also described himself and Mr Modi as "world leaders in social media".
Mr Modi said the fight to remove safe havens for terrorism was an important part of US-India co-operation.
He invited President Trump and his family to visit India.
Earlier in his trip to the US, Mr Modi met the heads of 20 US companies, including Apple's Tim Cook and Google's Sundar Pichai.
He told them that his government had pushed through thousands of reforms to make India "business friendly".
He later tweeted: "Interacted with top CEOs. We held extensive discussions on opportunities in India."
Although the US and India are both economic powerhouses, there are sharp differences on issues such as immigration and climate change.
In an article for the Wall Street Journal ahead of Monday's meeting, Mr Modi said India and the US were "mutually reinforcing engines of growth and innovation".
Photo: AFP Image (President Trump said he and Prime Minister Modi were "world leaders in social media)"