"The prime minister talked about our interest in having dairy technology from New Zealand," external affairs ministry spokesman Vikas Swarup said at a media briefing here.
Modi's meeting with Key was held on the sidelines of the fourth and final edition of the biennial Nuclear Security Summit, the first of which was held in 2010.
"As you know, New Zealand is one of the world leaders in food processing. Prime minister said that India is one of the world's largest producers of milk," Swarup said.
Modi said that when it came to processing milk, India was not too good and New Zealand could find a very good market in India since the food processing industry has been enabled to obtain 100 percent foreign direct investment (FDI).
Discussions between the Indian and New Zealand prime ministers also involved trade issues.
"The New Zealand prime minister said that they had concluded a very successful FTA (free trade agreement) with China some years back and he was very keen on signing an FTA with India as well," Swarup said.
The two prime ministers also discussed the promotion of tourism between the two countries given Bollywood's interest in New Zealand.
Modi also told Key that more and more Indian students should be encouraged to study in New Zealand as they felt safe there.
The Indian prime minister said that New Zealand could follow Australia's example of attracting Indian students.
Modi arrived here on the second leg of his three-nation tour on Wednesday night from Brussels where he attended the 13th India-European Union (EU) Summit and held a bilateral meeting with Belgian Prime Minister Charles Michel.
Leaders of 53 nations and four international organisations are attending the Nuclear Security Summit.(IANS)