With more and more Indian-language films being shot here, Mukherjee said his country is "getting acquainted with the stunning natural beauty of New Zealand".
Bridges said that New Zealand airlines now have the opportunity to code-share to seven Indian cities - Bangalore, Chennai, Hyderabad, Kochi, Kolkata, Mumbai and New Delhi.
"India is an emerging superpower, and its population of 1.25 billion people presents enormous opportunities for New Zealand," the minister said.
"Our annual trade with India is worth more than $1 billion. In the year to 31 March 2016, almost 52,000 Kiwis travelled to India and close to 60,000 Indians visited New Zealand. In addition, more than 160,000 people of Indian descent live here.
"Today's signing will boost tourism, trade and personal ties between our two countries," he said.
India New Zealand Business Council treasurer Bhav Dhillon said that getting a direct flight between the two countries would "change the paradigm" of both tourism and trade.
Air New Zealand, Air India and Singapore Airlines are among the operators which have the potential to run such a direct service.
"We are very confident that there will be a very robust growth in tourist numbers from India to New Zealand once we have a direct flight between these two countries," Dhillon told the Herald this week.
"Once's there a direct flight that will really change the paradigm in terms of tourism and trade, a direct flight reduces a lot of non-tariff barriers. We think a direct flight will solve a lot of issues on the trade front as well as on the tourism front."
Since the Government's Air Transport policy was introduced in 2012, Bridges said 50 new or amended air agreements had been negotiated, bringing the total to 78.
Most of the major airlines in the world are now able to operate services to New Zealand without restriction, with 18 new air routes announced in the past year alone.
"Our success in negotiating Air Services Agreements is providing New Zealand access to a large wealth of benefits including tourism and trade. We'll continue our efforts to grow and enhance these connections, making it easier for New Zealanders to travel and trade internationally."