"As two partners, we must also take advantage of our synergies to jointly face emerging regional challenges, and to exploit new opportunities," Modi said in a speech at a lunch hosted in his honour by Vietnamese Prime Minister Nguyen Xuan Phuc.
"It is a matter of great satisfaction that we have now decided to upgrade our relationship to a Comprehensive Strategic Partnership," he said.
Vietnam is India's country coordinator for the Association of Southeast Asian Nations (Asean).
Modi, who arrived here on Friday, said that "a strong India-Vietnam partnership would lead to prosperity, development, peace and stability for our people, and in the wider region".
"Vietnam is a strong pillar of India's Act East Policy," he said.
"Our bilateral ties are based on strong mutual trust, and understanding, and convergence of views on various regional and international issues."
Read More: India and Vietnam sign 12 agreements
Modi also referred to the ages-old people-to-people ties between the two countries.
"The linkages between our two countries have deep historical and civilisational roots, going back over 2,000 years," he said.
"These cultural bonds reflect themselves in many ways - most prominently, in the connect between Buddhism and the monuments of the Hindu Cham civilisation (in Vietnam)."
Stating that the India-Vietnam ties have been shaped by a strong desire for the progress and prosperity of the people, he said: "In India, we believe in sharing our knowledge, experiences and expertise with other developing countries. There can be no better example of this than in the success of our multifaceted bilateral cooperation with Vietnam over the last four decades."
Read More: Pics: Modi on a special visit to Vietnam
In this connection, the Prime Minister referred to the Cuu Long Delta Rice Research Institute in the Mekong Delta that was built with India's aid.
"India helped set up the institute in the Mekong Delta, sending agricultural experts and training its faculty in India," he said.
"Today, Vietnam is the world's third largest rice exporter. We are happy to have partnered with Vietnam in its emergence as a major rice producing and exporting country."
Earlier on Saturday, India and Vietnam signed 12 agreements, including on provision of patrol boats and on cyber security, following delegation-level talks headed by Modi and Phuc.
Read More: Modi visits Ambassadors' Pagoda in Vietnam
In a joint press statement with his Vietnamese counterpart following the signing of agreements, Modi said that India has extended a $500-million line of credit to Vietnam in the defence sector.
This is the first bilateral prime ministerial visit from India to Vietnam in 15 years after the visit of then Prime Minister Atal Bihari Vajpayee in 2001.