Modi welcomed Dung and his wife Tran Thanh Kiem at Rashtrapati Bhavan with a guard of honour, a statement from the Prime Minister's Office said.
Dung began his India visit by touching down at Bodh Gaya in Bihar on Monday. He is accompanied by a 50-member business delegation.
Modi also met the Vietnamese delegation.
MEA Spokesperson Syed Akbarruddin tweeted:
India-Vietnam Prime Ministers begin talks. pic.twitter.com/QPV8XRIDUl— Syed Akbaruddin (@MEAIndia) October 28, 2014