The West Bengal chief minister later stated that a "lot of issues" were discussed during the meeting.
"The discussion was friendly and cordial. We discussed trade, economic ties and their improvement among other things," she said.
"The country (Bangladesh) is doing well in all aspects and we want them to prosper more...We want them (Bangladesh leaders) to come here all the time," Banerjee told the journalists following the highly anticipated meeting.
The Trinamool Congress president said the responsibility of maintaining good relations between India and Bangladesh depend on both the countries.
Banerjee added that if the Centre and Bangladesh agreed, a 'Bangabandhu Bhavan' could come up in the city.
Hasina was on a two-day visit to India to attend the convocation of Visva-Bharati and the inauguration of Bangladesh Bhavan at Santiniketan on Friday. She also visited the Jorasanko Thakurbari, the ancestral house of Rabindranath Tagore in the city.
On Saturday, Hasina was conferred honorary D.Litt by Kazi Nazrul University in Asansol. She visited the Netaji Research Bureau at the national leader's ancestral house in the city prior to her meeting with Banerjee.
Hasina later left for Dhaka in a special flight.