The two leaders met yesterday on the sidelines of the ASEAN Summit in Manila, the Philippines.
The two leaders discussed the comprehensive strategic partnership between the United States and India and their shared commitment to a free and open Indo-Pacific region, the White House said in a statement.
"They pledged to enhance their cooperation as Major Defense Partners, resolving that two of the world s great democracies should also have the world's greatest militaries," it said.
President Trump expressed appreciation that Indian purchases of oil from the United States have surpassed 10 million barrels in recent months, and expressed confidence that stronger energy cooperation will be a geopolitical and economic game changer for both countries.
The first consignment of American crude oil reached India in October and Indian petroleum companies plan to purchase crude oil worth $2 billion from the US in the next one year.
Prime Minister Modi said that he looked forward to hosting the US delegation to the upcoming Global Entrepreneurship Summit, showcasing innovation and collaboration between the two countries.
The talks between President Trump and Prime Minister Modi came after officials of India, the US, Japan and Australia held their first meeting to give shape to the much talked about quadrilateral alliance to keep the Indo-Pacific region "free and open".
Giving details of yesterday's deliberations, Indian Foreign Secretary S Jaishankar in Manila said PM Modi and Donald Trump undertook "a broad review of the strategic landscape in Asia" without further elaboration.
Asked whether the formation of India-Australia-the US-Japan quadrilateral was discussed, Mr Jaishankar had said there was a passing mention of it, adding that the meeting of the officials of the four countries was part of diplomacy.
"It was a very expansive discussion," Mr Jaishankar said, adding that President Trump also shared his "impression" of his ongoing Asia trip which also took him to Japan and China.