While the new Kolkata flight and the third daily on the Mumbai-Abu Dhabi sector would start from February 15, the third daily from Delhi would begin on May 1, an Etihad release said.
Currently, the Abu Dhabi-based airline operates twice a day from the two busiest airports of Delhi and Mumbai.
Together, Etihad and Jet would connect Abu Dhabi to 14 Indian cities, with over 200 return flights each week, it said.
Etihad's Kolkata service would support its long-term development plan in India, even as Jet Airways has announced it would soon launch daily services between Abu Dhabi and Goa, Lucknow and Pune.
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The Gulf carrier would also upgrade its aircraft on some Indian routes, including introducing three-class, wide-body aircraft on select flights, besides flying its new Boeing 787 -9 Dreamliner on the Mumbai evening services in January 2015.
Commenting on the announcements, Etihad President and CEO James Hogan said, "India is expected to become the world's third largest air passenger market within the next 20 years, and we are focused on providing travellers with the best possible offering into and out of the country."
Regarding Jet-Etihad's partnership, Hogan said, "Both airlines' depth and breadth in India are stronger than any of our regional competitors and there are significant opportunities to increase our frequencies on existing routes, and introduce more Indian destinations into our network, which will set us even further apart from other airlines.