The three leaders launched the train through video conference.
A fully air-conditioned weekly passenger train service 'Bandhan Express' will run every Thursday from both Kolkata and Khulna.
On the occasion, Modi said the ties of friendship between India and Bangladesh have further strengthened.
Modi said in Bengali, 'Aaj ei shubho uplokkhe dui desh bashider amar abhinandan janai. Aaj amader moitreyee, bandhon aro sudriro holo' (I congratulate the people of the two countries on this auspicious occasion. Our ties of friendship got more strengthened today.)
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Hasina said, "Today is a great day for relations between the two countries with the inauguration of the train services and the two bridges. This train service is a dream come true for people on both sides of the border."
Chief Minister Mamata Banerjee described the launch as a remarkable day for India and Bangladesh.
"The relations between the two countries will strengthen in the future," she said.
Immigration and customs facilities were also inaugurated at Kolkata station.
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