Despite the upbeat rhetoric, the relationship between the two leaders has hit some initial snags. "American companies have likewise fueled their global growth by investing more than $20 billion in India", he wrote.
The president says trade between the two global powers must be "fair and reciprocal" and he is hoping barriers will be removed to the exports of USA goods to Indian markets.
This is in addition to the 22 Predator Guardian drones that the USA will supply to India. Trump said the countries would work to close the USA trade deficit with India.
Perhaps the most important outcome of their meeting will be putting to rest the notion that the U.S. -India relationship is adrift.
On Sunday, the Indian leader met with top American executives, painting for them a picture of a business-friendly India with "minimum" governmental encumbrances. Modi, under a program titled "Make in India", has been looking for foreign companies to set up production in India.
President Trump delivered a joint statement with Indian Prime Minister Modi at the White House Monday afternoon.
Although Modi's two-day Washington visit, which began Sunday, is lower key than his previous three trips to the USA since he took office in 2014, there will be plenty opportunity for face time with Trump.More news: Afghanistan: At Least Five killed as Taliban Storm Police Compound
Mr Trump has so far focused on outreach to China as he looks to Beijing to rein in nuclear-armed North Korea. But Washington and New Delhi share concerns about China's rise as a military power that has underpinned increasingly close relations in the past decade. The U.S. deficit in goods and services with India a year ago was about $30 billion. In a concrete indication of that, the U.S. State Department approved the $365 million sale of a C-17 military transport aircraft.
Modi harked back to Trump's "Make America Great Again" campaign slogan to stress that his agenda for his country was little different than Trump's. Mr Modi described the two countries as mutually reinforcing engines of growth and innovation in an uncertain global economic landscape.
"I'm nervous ... looking at this trip, you've got the leader of the world's wealthiest country expecting the leader of one of the world's developing countries to come here and give us benefits and gifts", said Richard Rossow of the Center for Strategic and International Studies before the visit.
"The relationship between India and the United States has never been stronger, never been better", Trump told reporters in the White House Rose Garden as he stood alongside the Indian premier.
Trump administration officials had pointed to both leaders' impact on social media - each has more than 30 million Twitter followers - as proof that they are cut from the same cloth, and predicted the two would get along well.
He said the designation of Salahuddin shows that Washington is willing to work closely with New Delhi on terrorism-related matters, although it remains to be seen if that signals a tougher policy toward Pakistan.
Trump's administration has meanwhile indicated it could take a tougher stance on Pakistan, which India has long accused of harboring militant groups.
Modi was expected to address issues of terrorism and, possibly, U.S. aid to Pakistan. After withdrawing from the Paris climate agreement, Trump lashed out in particular at India, insisting that it made its "participation contingent on receiving billions and billions and billions of dollars in foreign aid from developed countries".