The Prime Minister's Office said Obama reiterated his invitation to Modi to visit Washington in September and to work closely to make India-US relations a defining partnership for the 21st century.
Burns conveyed Obama's desire to boost economic ties with India, with a focus on next-generation technologies and manufacturing sector.
Burns said US sought India's cooperation in enhancing energy security; deepening security cooperation, including in maritime security, counter-terrorism and intelligence exchange; expanding consultation and coordination on Afghanistan; and, working more broadly for security and prosperity in Asia.
Modi thanked Obama for the invitation and looked forward to a "result-oriented" visit with concrete outcomes that impart new momentum and energy to India-US strategic partnership, the PMO said.
"Modi was of the view that re-energising the partnership between India and the United States would send an important message to the region and beyond. Articulating his vision for India-US relations, Modi stated that the relationship between the world's oldest and largest democracies should not only be for the benefit of the two countries, but should emerge as a powerful force of good for peace, stability and prosperity in the world," PMO added.
National Security Adviser Ajit Doval, Foreign Secretary Sujatha Singh, US Charge d'Affaires Kathleen Stephens, and Assistant Secretary of State for South and Central Asian Affairs Nisha Biswal were present at the meeting.