The invite comes ahead of Vietnamese Prime Minister Nguyen Tan Dung's visit to India in the last week of October.
In September, President Pranab Mukherjee had visited Vietnam.
India has also decided to open a Culture Centre in Hanoi shortly.
Tong Thi Phong, Vice-President of National Assembly, extended the invitation to Deputy Chairman of Rajya Sabha P J Kurien after a meeting on the sidelines of the ongoing 131st Union (IPU) on October 14.
Both the leaders expressed satisfaction over the ongoing parliamentary cooperation and discussed the possibility of further enhancing cooperation through regular interaction, including cooperation through the ASEAN Inter-Parliamentary Assembly (AIPA) platform.
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He also discussed about the ongoing bilateral relations covering cooperation in economic and commercial and cultural fields as well as people-to-people contacts.
Both the leaders recounted that the bilateral relation is strongly rooted in close contacts between the leaders of the two countries since the time of independence and duly strengthened by regular high level exchanges.
The Rajya Sabha Deputy Chairman conveyed that India looks forward to the important visit of the Prime Minister of Vietnam later this month.