The two countries also signed three other agreements -- to enhance aviation links, to jointly work in the area of energy efficiency and promotion of parliamentary cooperation.
The four pacts, aimed at boosting the relations, were signed here in presence of Lok Sabha Speaker Sumitra Mahajan and visiting President of Vietnam's National Assembly Nguyen Thi Kim Ngan after their talks on enhancing the ties.
Modi recalled his earlier meeting with Ngan in Hanoi during his visit to Vietnam in September.
He said that Ngan, as the first woman to head the National Assembly of Vietnam, is a source of inspiration to women across the world.
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Modi welcomed increased Parliamentary interactions between India and Vietnam, and called for instituting an exchange programme for young parliamentarians of the two countries.
Vietnam is the 14th country with which India signed the
civil nuclear deal.
From the Indian side, the MoU on civil nuclear cooperation was signed by Sekhar Basu, Secretary of Department of Atomic Energy, while Pham Cong Tac, Deputy Minister of Science and Technology, signed it from the Vietnamese side.
The two countries had earlier in 1986 signed a pact in the civil nuclear field which was limited to training. However, the new agreement is broadbased and encompasses research on nuclear reactors, sources said.
An MoU on 'Promotion of traffic between Vietnam and India and sharing of best practices in airline operation, ground handling procedure and management' was also signed between Air India and Vietjet Aviation Joint Stock Company.
Energy Efficiency Services Limited (EESL), a PSU under the Power Ministry, and Vietnam Electricity (EVN) signed an MoU on 'Developing a Partnership to Jointly Work in the Area of Energy Efficiency'.
It was signed by Satish C Mehta, Senior Advisor in EESL, and Duong Quang Thanh, Chairman of Vietnam Electricity.
The Speaker pitched for enhanced engagement between the two countries and specified sectors like defence, security, energy, exploration, non conventional energy as some of the key areas of mutual benefit.
"India and Vietnam can mutually benefit from each other's strength," she said.
Referring to South China Sea over which China is laying an absolute claim and is in confrontation with Vietnam and some other East Asian countries, Mahajan said India has persistently maintained that sea lanes of communication passing through that maritime area are critical for peace, stability, prosperity and development.
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"Vietnam is playing an increasingly important role in global economic affairs," the Speaker said, according to a press release issued by the Lok Sabha Secretariat.
With India's 'Look East' policy evolving into an 'Act East' policy, this region has assumed even greater importance in India's strategic thinking and economic engagement, she said.
She hailed the "exceptional economic rise of Vietnam by grit and hard work coupled by its warm and friendly people" and said it is indeed inspiring and heart-warming.
Noting that India and Vietnam have a healthy tradition of parliamentary exchanges and cooperation, she said this visit has added to the ever-growing friendship and goodwill between our two countries and their peoples.
"The Parliament of India looks forward to sustaining this momentum," she told the Vietnamese delegation which witnessed proceedings of the Rajya Sabha earlier in the day.
Ngan thanked the Speaker for the warm traditional hospitality extended to her delegation and hoped that the ongoing visit will further consolidate and strengthen bilateral relations between the two countries.