Relations with China are a major issue shared by Modi and Abe, as their cooperation may balance China's growing regional influence and military assertiveness.
Reports say that India and Japan are likely to sign key agreements in maritime security and defence cooperation, including a mutual logistics support agreement.
During Modi's summit with Abe on Sunday, New Delhi and Tokyo will review the progress in ties and seek to deepen the strategic dimensions of the bilateral relationship. Japan is India's most trusted partner in its economic and technological modernisation, he said.
PM Modi is in Japan to attend the 13th India-Japan annual two-day summit. Abe hosted a luncheon for Modi at a scenic resort near Mount Fuji, after which they visited a robot factory, PTI reported. "Go to Bhubaneshwar and cheer up the Indian team and also encourage each team there", Modi said.
The Japanese Foreign Ministry said the leaders had lunch at a hotel in Yamanashi Prefecture, west of Tokyo, and exchanged a wide range of views on pursuing "a free and open" Indo-Pacific region.
"Just as how lamps light up the dark during Diwali wherever you are, you are spreading the light of India to every corner of the world and Japan and making the country proud".More news: Indonesian Lion Air passenger flight crashes into sea soon after take-off
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Japan's role in India's economic journey continues to be integral to its transformation, Kumar added.
The PM will then meet the heads of Japanese venture capital companies and captains of Japanese industry before attending a meeting with the representatives of the India-Japan Business Leaders Forum. This is the 12th meeting between the two leaders in the last four years.
Following the talks, agreements were signed on cooperation between the naval forces of the two countries, healthcare, digital and new technologies, and food processing.
India is also hoping to have some kind of synergy or integration between Modi's Ayushman Bharat scheme, which is the largest medicare programme of its kind globally, and the Japanese programme which is called Asia Health and Wellbeing Initiative.
Prime Minister Narendra Modi will return to India today.
Describing Japan as the confluence of the best aspects of eastern and western civilisations, PM Modi said that the country has taught that the path to the development of mankind is not a conflict between the ancient and the new, but its co-existence and creation.
The Indian prime minister arrived in Japan earlier in the day.