Modi also separately invited Trump's daughter Ivanka to the U.S. delegation to the Global Entrepreneurship Summit in India that will be held later this year.
Responding to this Modi added that, Indian government has initiated as many as 7000 flagship programes and reforms and that now India was proving a easy platform to all to do business in the country.
In a joint briefing following their one-on-one meeting and delegation-level discussions at the White House, Modi said "We talked about terrorism, extremism and radicalisation and agreed to cooperate on this".
The two leaders, who held a meeting at the White House on Monday, also "called on all nations to resolve territorial and maritime disputes peacefully and in accordance with global law", the statement said.
Thanking Trump and the First Lady, Melania, again for the grand welcome rendered to him, Prime Minister Modi said, "I would like to thank President Trump for his kind words about India". He said that "I'm proud to announce to the media, to the American people and to the Indian people that Prime Minister Modi and I are world leaders in social media".
In a tweet, Mr Trump described Mr Modi as a "true friend".
In this context, the phrase "Kashmir to Kanyakumari" that is cited not by Modi alone but many other leaders, is not completely accurate either.
Apple has not disclosed how much revenue it generates in India but said that sales grew by "strong double digits" there in the most recent quarter.
Trump said both countries have been struck by the "evils of terrorism", and are determined to destroy terrorist organizations and the radical ideology that drives them.
"I will also call on King Willem-Alexander of the Netherlands and meet Queen Maxima", he had said in a Facebook post before leaving on his three-nation trip. India and the United States will always be tied together in friendship and respect.
The United States also has offered to sell a naval variant of the Predator drone made by USA defense contractor General Atomics Aeronautical Systems, the White House said in a statement, a deal that would be worth more than $2 billion.
The meeting brought together two nationalist leaders who have made efforts to boost their domestic manufacturing industry signature issues.
In a late night statement, the White House said completion of these sales would increase bilateral defence trade to almost United States dollars 19 billion, supporting thousands of U.S. jobs.
Bibi said that Modi's upcoming visit to Israel would mark a change in the country's status.
Addressing Trump directly, Modi offered his "deep appreciation" for the President's "strong commitment to the enhancement of our bilateral relations".
"The top priority for both President Trump and myself is to protect our society from global challenges like terrorism", Modi said.
Meanwhile, Modi will be hoping that as well as tackling the Islamic State, Trump will step up pressure on militant groups based in Pakistan accused of launching attacks on India. "Towards this end, we shall take steps to further strengthen our successful digital partnership", Modi said in a joint statement.