The dinner at the Prime Minister's official residence at 7 Race Course Road was attended by Abe and his wife Akie, who joined Singh and his wife Gursharan Kaur.
Abe had hosted a similar dinner for Singh and his wife during the Indian leader's visit to Japan in May last year.
Tomohiko Taniguchi, Councillor in Japan's Cabinet Secretariat and part of Abe's delegation, said the premier's trip to India was to pay tribute to the "tremendous accomplishments" of Singh.
Talking about the significance of Abe's visit, he said, "First of all it is to pay tribute to the tremendous accomplishments of Prime Minister Singh, who Shinzo Abe has for many years regarded as one of his mentors. Knowing that Prime Minister Singh is soon ending his political career, Shinzo Abe wanted to pay a tribute to him."
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Taniguchi recalled Abe's 2007 visit to India, during which his health had deteriorated.
"To me Abe looks like a born-again politician not in the religious sense of the word but in the physical terms," he said.
The Japanese official spoke about gestures made by Singh that left a "lasting impression" on Abe. "When Abe was ill during his India trip in 2007, Singh showed a sympathetic attitude," he said.
When Abe made his next visit to India while not in office, Singh was just about to leave for a UN General Assembly session. However, Singh arranged for five to six Cabinet members to meet Abe at short notice, Taniguchi said.
Singh and Abe held extensive talks here yesterday on bilateral, regional and global issues.
Abe, 59, today became the first Japanese Prime Minister to attend India's Republic Day celebrations as chief guest.