The prime minister met Pranab at the Rashtrapati Bhavan on Sunday, the third day of her stay at the president's residence during her state visit.
The deep relations between Bangabandhu Sheikh Mujibur Rahman's daughter Hasina and Pranab developed long before he became president. She calls him 'Dada', a term used in Bangla to address an elder brother.
Hasina also remembered Pranab's role in Bangladesh's War of Independence as a leader of the Congress party.
Bangladesh has conferred 'Liberation War Honour' on Pranab in recognition of his contribution. He is also connected to Bangladesh through his marriage. His wife late Suvra Mukherjee hailed from Narail.
The Indian president expressed gratitude to Hasina for attending the funeral of Suvra in New Delhi two years ago.
Briefing the media after the meeting, Prime Minister's Press Secretary Ihsanul Karim said Pranab lauded Hasina for her efforts to give a solid foundation to the relations between the two countries.
Karim said they also discussed the consensuses, agreements and memoranda of understanding reached in and after the bilateral meeting between Hasina and her Indian counterpart Narendra Modi.
After the meeting with Pranab, Hasina joined a ceremonial dinner hosted by
the president in her honour. Indian Vice-President Hamid Ansari and Modi also
joined the dinner at the Banquet Hall. They watched a cultural programme at the
Ashoka Hall before the banquet.
The guests also included Indian Chief Justice Jagdish Singh Khehar, Lok Sabha
Speaker Sumitra Mahajan, Home Minister Rajnath Singh, Minister of State for Heavy
Industry Babul Supriyo, West Bengal Chief Minister Mamata Banerjee, and Indian
Army chief General Bipin Rawat.
New Delhi has put special emphasis on the visit. The prime minister is staying at the Rashtrapati Bhavan at Pranab's invitation, which is considered 'exceptional'.
Earlier in the day, Congress President Sonia Gandhi met Hasina at the Rashtrapati Bhavan.
The prime minister is scheduled to return on Monday.