The two leaders discussed a range of issues, including cooperation in the field of nuclear energy.
Earlier in the day, External Affairs Minister Sushma Swaraj called on the Vietnamese president.
Their discussions focused on steps to further strengthen country's comprehensive strategic partnership by expanding cooperation across all sectors, Ministry of External Affairs Spokesperson Raveesh Kumar said.
Mr Quang was also given a ceremonial reception at the Rashtrapati Bhavan.
"PM @narendramodi welcomes Vietnamese President Tran Dai Quang on his first State visit to India at the Hyderabad House ahead of the bilateral talks. India and Vietnam enjoy warm and cordial relationship with common roots in history. #ActEastPolicy," Mr Kumar tweeted.