After the talks, the two countries will sign a number of agreements and MoUs for cooperation in diverse areas, including defence and civil nuclear energy.
Earlier, Modi announced India's commitment to extend $500 million credit for the defence procurement of Bangladesh.
"Along with our shared land boundaries are our shared rivers", Modi said while jointly addressing the media with Bangladesh Prime Minister Sheikh Hasina following bilateral talks in Delhi.
"We discussed the issues of water resources management including the sharing of water of common rivers, including Teesta, the Padma-Ganga barrage project and basin management of the common rivers". We want peace, prosperity and progress for our neighbors as well. "In implementing this line of credit, we will be guided by Bangladesh's needs and priorities", he said. We are a long-standing and trusted development partner of Bangladesh.
Highlighting energy security as an important dimension of India-Bangladesh development partnership and that India would play a role in helping Bangladesh, Modi said the two countries had on Saturday added an additional 60 MWs (megawatts) of power to the 600 MWs of power already flowing from India to Bangladesh.
The visiting Prime Minister said she was grateful to the people and the government of India for their contribution to her country's liberation.
The Bangladesh Prime Minister stressed that the main intention of the two countries is to improve the living conditions of the people of South Asia.
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To the Modi government, Mamata's decision to accept the Prime Minister's invitation to attend a series of inaugurations - a train and a bus connecting Calcutta and Khulna and a new rail rake - signalled her openness to the negotiations over a resolution.
-PM Modi said Bangaldesh's zero tolerance policy towards terrorism is an inspiration. "And, steps are being taken to put into operation the coastal shipping agreement". An agreement was also signed on peaceful use of nuclear energy.
He said that 17 projects have been identified for utilisation of the new line of credit.
This is the Bangladesh Prime Minister's first bilateral visit to India in seven years since her last visit in 2010.
Before the function, Modi and Hasina met and posed for photographs with Major Ashok Tara of 14 Guards who had rescued the family of Bangladesh founder Sheikh Mujibur Rahman from a house in Dhanmandi where they had been imprisoned by the Pakistani soldiers in 1971.
PM Modi announced a special medical scheme under which 100 "Muktijoddhas" (warriors of the liberation war) of Bangladesh will be provided medical treatment in Indian hospitals every year.