The two leaders met on the sidelines of 13th ASEAN-India Summit here in the Malaysian capital.
"Working through lunch with an old friend. PM @AbeShinzo hosts PM @narendramodi for the second bilateral," External Affairs Ministry Spokesman Vikas Swarup tweeted.
Earlier Modi met his Chinese counterpart Li Keqiang.
"The India-Japan relationship has the greatest potential of any bilateral relationship in the world," Abe was quoted by Swarup as saying.
The meeting comes ahead of Abe's visit to India on December 11 to hold annual summit talks with Modi and take further the already close relations between the two major Asian economies.
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"I today express my commitment that over the next three years, Japan will assist as many as 40,000 young people from India, ASEAN and elsewhere in Asia in improving their technical skills and acquiring knowledge," Abe said at a separate event.
He emphasised that for Japan, "Asia is no longer a recipient of assistance" It is instead our partner for growing together.
"The large scale state-of-the-art coal fired thermal power station planned for India's southeast region is a project that will exceed 500 billion yen," he said.
