At the same time, Bangladesh Prime Minister Sheikh Hasina provided 10 GB Internet bandwidth to India and the entire programme was held through video-conferencing.
"In this age of interdependence, the two countries would further strengthen its ties and it is a significant day that both are promoting the ways of development," Modi said.
Hasina said that "the relation between the countries has further consolidated through the supply of power and Internet bandwith."
"Bangladesh would observe its National Day on March 26 and I pay my respect to the memory of the Father of the Nation of Bangladesh. The era of good relations began during the time of 'Bangabandhu' between the two countries which still continues," Modi said.
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The eight north-eastern states would be immensely benefited with the opening of the third International Internet gateway, he said, adding that Bangladesh, India, Nepal and Bhutan have made considerable development in road links.
"Now India and Bangladesh is connected through water, surface communication and air. We want to be connected with Bangladesh though space also," the Prime Minister said.
He said the festival of Holi has started in India and Bangladesh and both would be coloured with new colours.
Hasina, in her speech, said, "We always remember India's cooperation during the liberation movement in 1971."
On power supply, she said during her visit to Tripura in 2012, she discussed the matter of getting power from the state's Palatana project.
Hasina said her country was getting 500 MW power from India now and both the countries made considerable development in the field of cooperation through roads, railways and power.
She also thanked Prime Minister Modi and Tripura Chief Minister Manik Sarkar for their cooperation.
After the formal opening of international gateway of Internet, Tripura became the third state having such a gateway after Mumbai and Chennai.
Telecom Minister Ravi Shankar Prasad had laid the foundation of the project in Agartala on July 13, 2015 that aims at strengthening telecom services in NE states.
Under the project, an international gateway for broadband connectivity has been set up at Agartala in which connectivity will be provided through Bangladesh under a pact between BSNL and Bangladesh Submarine Cable Company Limited.
The cost of the project is Rs 19.1 crore and annual operational expenditure is around Rs 7.2 crore. The bandwidth of 10 GB can be extended up to 40 GB, officials said.
Power Grid Corporation erected 47 km long 400 kv double circuit transmission lines from Suryamaninagar powergrid near here to Comilla in Bangladesh.
The 726 MW gas-based thermal power project at Palatana in Gomati district is run by ONGC Tripura Power Company.