Modi and Abe met on the sidelines of 13th ASEAN-India Summit Kuala Lumpur in the Malaysian capital as the Japanese Premier hosted a luncheon for his Indian counterpart.
Abe described the Indo-Japan ties as having the "greatest potential of any bilateral relationship in the world."
Abe said he personally wanted to expand the Indo-Japan Special Strategic and Global Partnership.
Prime Minister Modi also expressed India's keenness to work with Japan and invited Japanese firms to take part in the 'Make in India' programme especially in the defence sector, External Affairs Ministry Spokesperson Vikas Swarup told a media briefing in Kuala Lumpur.
Noting that Maruti Suzuki had transformed the automotive industry in India, Modi said in the last half a century all the major transformations in the world had a Japanese role.
The two leaders also talked about regional connectivity and maritime security and in this regard the South China Sea issue came up for discussion, Swarup said.
India wants all parties to the disputes in the South China Sea to abide by the guidelines on the implementation of the Declaration on the Conduct of Parties in the South China Sea, he said.
India supports efforts for the early adoption of a Code of Conduct on the South China Sea on the basis of consensus.
The two sides also reviewed bilateral defence ties and referred to the recent Malabar naval exercises, Swarup said.
Modi acknowledged the Japanese Premier's vision for the bilateral relationship, and said he looks forward to Abe's visit to India in December.
The Prime Minister said that Japan was partnering India in a number of initiatives such as the Delhi Mumbai Industrial Corridor (DMIC), which had transformative potential.
The upcoming CoP-21 conference in Paris, reform of the UN Security Council and the issue of terrorism also came up for discussion.
Deepening the Varanasi-Kyoto partnership also came up in the discussions. The two cities have been declared as twin cities.
"Meeting PM @AbeShinzo is always a delight. Had comprehensive talks with him at the lunch he hosted," Modi tweeted about his meeting with Abe.
Modi had visited Japan last year during which that country had announced doubling of its private and public investment in India to about USD 34 billion over a period of five years.
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