The meeting came just weeks after U.S. Secretary of State John Kerry came to India to lead a strategic dialogue between the nations. The pair of high-profile meetings signal increasing efforts to upgrade bilateral relations as the U.S. lays out its plans to rebalance its foreign policy toward the Asia-Pacific.
Mr Biden's trip will also lay the groundwork for a summit meeting between Singh and President Barack Obama in Washington in September.
Indian officials said the two discussed a raft of issues, including ways to boost trade and ease bottlenecks preventing American companies from investing in the Indian market.
They also talked about the hurdles in implementing a landmark civil nuclear agreement that the countries ratified in 2008.
India has said foreign nuclear companies operating in the country should assume nearly unlimited liability for accidents, a stringent condition that makes it all but impossible for foreign nuclear firms to set up nuclear power plants in India.
Regional security, especially in war-torn Afghanistan, and New Delhi's concerns about the possibility of the Taliban returning to power in Kabul post-2014, were also discussed during the 75-minute meeting.
The U.S. increasingly views India as a partner in developing Afghanistan, where New Delhi has provided $2 billion in assistance. Washington wants India to play a more active role in training Afghan security forces as the U.S. and its NATO allies withdraw combat forces by 2014.
Later on Tuesday, Biden will attend a banquet in his honour hosted by his Indian counterpart, Vice-President Hamid Ansari, before leaving for Mumbai.
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