Modi also announced $500 million for defence procurement after bilateral talks in New Delhi with Bangladesh Prime Minister Sheikh Hasina who is on a four-day visit to the country.
China has been the biggest source of defence purchases for Bangladesh for many years. Wary of China's growing interest in India's backyard, Modi has been keen to play a greater leadership role in South Asia since coming to power in 2014.
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In 2015, Modi signed a historic land border pact with Dhaka, removing a major irritant and infusing a new warmth between the two countries that share a 4,097 kilo metre-long porous border.
"India has always stood for the prosperity of Bangladesh and its people. We are a long-standing and trusted development partner of Bangladesh," Modi said at a press briefing after the sides signed as many as 22 agreements in key sectors including civil nuclear energy.
"In this context I am happy to announce a new concessional line of credit of $4.5 billion for the implementation of projects in priority sectors for Bangladesh."
"This brings our resource allocation for Bangladesh to more than $8 billion over the past six years."
There was no breakthrough however in a long-standing dispute about the sharing of water from the Teesta river which flows through both nations although Modi vowed to find a solution to the issue seen as vital for Bangladesh farmers. The deal was aborted at the very last minute during former Indian prime minister Manmohan Singh's visit to Bangladesh in 2011 and has been in the doldrums since.
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Hasina, whose Awami League is historically seen as more sympathetic to India than the arch-rival Bangladesh Nationalist Party, said the two countries will jointly produce a documentary on the 1971 War of Liberation of Bangladesh, a move that is likely to irk Pakistan.
Hasina is the daughter of Sheikh Mujibur Rahman, who led Bangladesh to independence from Pakistan in 1971.
The government says that up to three million people died in the independence war, many killed by Bangladeshis who collaborated with Pakistani forces. India's intervention on behalf of Bangladesh's independence fighters proved decisive in that conflict.
"We are committed to expand our relationship with India," said Hasina. "The entire South Asia region will be a beneficiary of our friendly relations and cooperation."
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