Here are the latest developments:
The two leaders visited Varanasi's Dashashwamedh ghat for a cultural programme and the traditional "Gangaarti". Later, they attended a pure vegetarian Banarasi banquet, where Uttar Pradesh Chief Minister Akhilesh Yadav, Governor Ram Naik and state ministers were present.
Earlier today, India and Japan signed a number of agreements included one on civil nuclear energy cooperation, India's first bullet train and transfer of defence equipment and technology.
"The memorandum on civil nuclear energy cooperation is more than just an agreement for commerce and clean energy. It is (a) shining symbol of a new level of mutual confidence and strategic partnership," PM Modi said. The formal signing of the agreement has been put off citing the need to finalise technical details.
The defence agreements not only involved the transfer of equipment and technology, but also brought in Japan as a regular partner in the Malabar Naval exercises, which so far has been between India and the United states.
The bullet train deal -- which involves a $12 billion package and technical assistance from Japan -- gives it an early lead over China, which is conducting feasibility studies for high speed trains on other parts of the Indian rail network.
While releasing the joint statement, PM Modi said bullet trains "will revolutionise Indian Railways... and become the engine of economic transformation in India".
The bullet train network will link Mumbai and Ahmedabad and is expected to cut travel time on the 505-km route from eight to around three hours.
This morning, PM Modi and Mr Abe met a group of top business leaders from both countries -- India-Japan Business Leaders Forum.
PM Modi said for the first time, Japan will import cars from India. "Maruti (Suzuki) will manufacture here... the Japanese company will manufacture here and export it to Japan," he said, adding that both India and Japan should move ahead together, not just in the sphere of high-speed trains, but also for "high-speed growth".
PM Abe said a "strong India is good for Japan and a strong Japan is good for India," and praised PM Modi's economic policies, saying they were "safe and reliable like Shinkansen-high speed trains."