There was much speculation if Dr Singh would meet Castro after the ailing leader did not attend the 14th Non-Aligned Movement summit. His brother, Defence Minister Raul Castro, chaired the meeting in his absence.
The 80-year-old Castro spent 40 minutes with Dr Singh in hospital and the leaders discussed various issues.
"I had gone there only to greet him," Dr Singh told journalists accompanying him on Air-India One, "but he engaged me in intense discussion. We discussed India's development prospects and how we are dealing with our population, food and energy problems. I will always remember this meeting. I felt I was in the presence of one of the greatest men of our times."
Castro has always shared a special relationship with India, be it with Indira Gandhi -- who he famously enveloped in a bear hug at the 1983 NAM summit in New Delhi -- or with her father Jawharlal Nehru.
This was Dr Singh's second meeting with Castro; he had met the Cuban leader earlier in his avatar as a bureaucrat.
Asked how well Castro was, Dr Singh said, "He was weak and in a wheelchair. He told me he was recovering well. He thought that had the NAM summit been held two days later, he would have been able to preside over it."
Castro surprised Dr Singh by requesting a photograph. The old revolutionary got up from his wheelchair for the photograph. "I want this picture to be seen by all of India," Castro told the prime minister.
When asked if the two leaders had condemned the US' continuing blockade against Cuba, Dr Singh said, "We did not go into any condemnation. He did, however, say that the world's financial system is faced with many uncertainties with countries like the US absorbing the bulk of the world savings and there was a risk about the future of such a financial system."
Dr Singh felt there were a lot to be done in India's social sector development when compared to Cuba's achievements for its people.
"There is a big backlog of illiteracy, of improving health standards, of reducing infant mortality rates if we expect our country to be better than what we are now," the prime minister said. "I am concerned about the distance we have to travel on these points."