The meetings took place on the sidelines of the ASEAN summit in the Philippines.
In the meeting with Turnbull, Modi is also understood to have discussed convergence of strategic interest of both the countries in the Indo-Pacific in the backdrop of China's aggressive military posturing in the region.
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The issue also figured during talks between Modi and US President Donald Trump here yesterday.
"A strategic partnership defined by close co-operation and multifaceted interaction. Prime Minister @narendramodi and Prime Minister @TurnbullMalcolm meet in Manila, discuss close cooperation to optimise significant potential for further cooperation across a broad range of areas," external affairs ministry spokesperson Raveesh Kumar tweeted.
A number of issues including bilateral cooperation in defence and security sphere were discussed in Modis meeting with his Vietnamese counterpart.
"Strengthening comprehensive strategic partnership. Prime Minister @narendramodi and Prime Minister Nguyen Xuan Phuc of Vietnam shared common goal to deepen bilateral relations between the two countries," Kumar said in another tweet.
The Modi-Phuc meeting came days after Trump's visit to Vietnam where he offered to mediate in the South China Sea dispute between several ASEAN member countries including Vietnam and China.
China claims sovereignty over all of the South China Sea, a huge source of hydrocarbons. However, several ASEAN member countries including Vietnam, the Philippines and Brunei have counter claims.
India has been supporting freedom of navigation and access to resources in the South China Sea in accordance with principles of international law, including the 1982 UN Convention on the Law of the Sea.
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