Free trade negotiations with India started in 2010 and have struggled over 10 negotiation rounds with no end in sight.
"I think it needs that push from the top to give it that reason for the negotiators to put their shoulder to the wheel," Key told New Zealand media.
New Zealand was pursuing trade deals like the one with India because "we don't want to have all our eggs in the Chinese market", Key said.
Easing steep agricultural tariffs would be extremely controversial in India, the world's largest producer and consumer of milk with millions of small-scale farmers.
"We are not there to put anyone's farmers out of business," Key said of that opposition.
"What we can do is strengthen and improve their capacity to produce their own food.
If they really want to leverage and grow rapidly the capacity to produce food, probably the best thing they could do is have an FTA with New Zealand.
"It is always the thing that countries worry about. But pretty soon they come to realise we are not there to put them out of business, we are there to work with them."
The plane breakdown caused the Mumbai leg of Key's trip to be cancelled, and as a result one member of the 35-strong business and education delegation returned to New Zealand.
Key said he sat down with delegation members after the changes were confirmed and they were "both understanding and realistic".
"Most of them have opportunities in Delhi. They would probably say the single most important thing I can do to help their business is to advance the relationship between New Zealand and India."
The Indian Government was "terribly understanding" about the delay, Key said, and the main focus for them was his meeting with Modi.
Compromise nearing on nuclear membership?
In the lead-up to the trip, Indian media have focussed on a sensitive point in the two countries' relationship: New Zealand's stance on an American-led push for India to join a club of countries that control access to sensitive nuclear technology.
The 48-member Nuclear Suppliers Group (NSG) sets global rules for international trade in nuclear energy technology, and was established in 1974 as a response to India's first nuclear test.
New Zealand is a member of the NSG.
India wants in, despite not being a member of the Nuclear Non-Proliferation Treaty, which requires members to make commitments on nuclear disarmament and non-proliferation.
It needs a unanimous vote to join, and has been blocked by Beijing, who has argued signing the non-proliferation treaty is a pillar of the group, and the rules shouldn't be bent for India.
Key has said New Zealand and other "like-minded" countries had said it was possible for India to join without signing the treaty, but that would require them to agree to meet similar conditions.
Joining the NSG is seen as a key test of Modi's foreign policy, and a report by the Economic Times, the world's second most-read English language business newspaper, quoted well-placed sources as saying the "primary objective of hosting Key is to elicit his country's support for NSG membership".
"It is understood that while the top Kiwi political leadership is favourably disposed to India's entry, the New Zealand foreign ministry has been dragging its feet on the matter because of India's non-NPT status," the August report stated. "India is hoping Key's visit would help bridge that gap."
In 2008 New Zealand was among the last NSG members to approve a one-off waiver from the NSG, which gave India most of the benefits of membership to the group.
China was opposed to that move, instead backing a bid by Pakistan, India's military rival, to join.
Key's meeting and the nuclear club membership discussion comes as the relationship between India and Pakistan deteriorates, following an attack last month on an Indian military base by militants India says were from Pakistan.
In response, Pakistan this month went as far as imposing a blanket ban on Indian shows.
Modi, India's 14th prime minister and a Hindu nationalist, has previously lobbied Key on the nuclear issue, as has US President Barack Obama.
The US position is India needs a sustainable energy alternative to coal power for its 1.3 billion people, and that it is a stable democracy.
Key has rejected the idea that New Zealand softening its stance could be a possible bargaining chip in free trade negotiations.
