"A renewed warmth with Vietnam. PM @narendramodi and PM Nguyen Xuan Phuc meet for a tete-a-tete before formal talks," External Affairs Ministry spokesperson Vikas Swarup tweeted.
This is the first bilateral prime ministerial visit from India to Vietnam in 15 years since the visit of then premier Atal Bihari Vajpayee in 2001.
Modi, who arrived here on Friday evening, on Saturday morning started by laying a wreath at the Monument of National Heroes and Martyrs here.
He also visited the much revered stilted house where Vietnamese icon Ho Chi Minh lived.
Modi was then accorded a ceremonial welcome with a guard of honour at the Presidential Palace in Hanoi.