The decision came following a meeting between visiting Vietnamese Defence Minister Gen Ngo Xuan Lich and his Indian counterpart Manohar Parrikar, defence sources said.
This is the second major training programme after the Vietnamese Navy was trained by the Indian Navy in operating Russian-origin kilo-class submarines. Both use Su-30 fighter aircraft.
It was not clear if there was any forward movement on the possible sale of BrahMos missiles.
Vietnam, which is involved in a territorial dispute with China, is keen to get it hands on the supersonic missiles that can be fired on land, water and under water.
Russia, which is a partner of India in development of BrahMos missiles is also okay with the deal.
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