The dignitaries also inaugurated the International Passenger Rail Terminal, End-to-End Immigration and Customs Clearance Facilities (for the passengers of Maitree Express and Bandhan Express) at Kolkata station, under India-Bangladesh Cooperation in Railways.
Hasina said she was also happy that two railway bridges at Bhairab and Titas are also being inaugurated which will contribute to faster connectivity between Dhaka and Chittagong.
"I hope this fine display of mutuality of our relationship will further strengthen our bilateral relations".
Indian Prime Minister Modi said, India takes pride in being a reliable partner in Bangladesh's development.
Calling it a historic day, Mamata Banerjee said that with the initiation of the new train service the bonding between the two countries will become further stronger.
The global rail Ppassenger terminus at Chitpur in Kolkata will make it possible for Indian passengers traveling to Dhaka or Khulna in Bangladesh by Maitree Express or the newly launched Bandhan Express to get immigration clearance before boarding the trains. "Our two countries are also working to re-open our pre-1965 rail links for cargo transport between Bangladesh and India".
"I have always said that protocol must not come in the way of bilateral relations, especially when it comes to interactions with neighbors, and when it is aimed at achieving development and progress", Modi said.
The bridge over the Titas was built by Indian company Gammon-Flcl Consortium.
Earlier, Modi began his speech breaking into Bangla. "Aaj ei shubho uplokkhe dui desh bashider amar abhinandan janai. Aaj amader moitreyee, bandhon aro sudriro holo".
Indian External Affairs Minister Sushma Swaraj was present at the New Delhi office while Bangladesh Foreign Minister AH Mahmood Ali, PM Hasina's Political Affairs Advisor HT Imam, and Economic Affairs Advisor Dr Moshiur Rahman, were present at the Hasina's official Ganobhaban residence.
The two railway bridges have been built at a cost of $100 million, which has been met from India's $8 billion soft loan to Bangladesh.
Our Benaploe correspondent adds: The Bondhon Express began its trial run from Kolkata with an 18-member Indian delegation on board.
Dhaka - Bangladesh and India have restored a railway connection more than five decades after it was suspended because of a war. The train reached Benapole at 1:30pm.
The Bandhan Express is scheduled to ply the route every Thursday.
The draft complaint also states that he was promised another two year deal which would have earned him $511,000 (£389,000). He is reportedly suing her for sexual harassment and hurling racial insults at him, among several other allegations.
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