Mr Key said South Korea could also take advantage of New Zealand's ability to produce good food.
Talks have been on hold for the past two years while South Korea completed agreements with the United States and Europe. Mr Key is using his trip to Seoul for the Nuclear Security Summit to try to ensure those talks begin again.
He said there was some urgency because Korea was a big market for New Zealand and South Korea was also negotiating with others, including Australia, Canada and Turkey.
"We can't afford to get left behind."
He said the main problem was the farming lobby in Korea - the perennial sticking point for New Zealand free-trade agreements. However, New Zealand had opposite seasons to South Korea, did not produce rice and had only a small portion of grain-fed beef - two of the main issues for South Korean farmers. He said food security was a significant issue for South Korea and New Zealand could help that.
"The reality is some very large companies who operate in this market are only just clinging on. So you look at someone like Fonterra or Zespri, they won't last in this market beyond a few years unless an FTA is completed. The tariffs are just too great."
He said Zespri had paid $34 million in tariffs last year. The average tariff was 45 per cent while Chile paid only about 12 per cent.
There was only a small window in which to finalise an agreement. He did not expect any action before South Korea's National Assembly elections next month, but said there was then a small window before the presidential elections in December during which an agreement could, in theory, be reached.
President Lee Myung-bak has voiced support but he will be replaced in December when presidential elections are held. South Korean presidents can serve only one five-year term, and Mr Lee's replacement is expected to be Park Geun-hye, the leader of the ruling Saenuri Party.
Mr Key said it was the official Year of Friendship between New Zealand and South Korea. He also hoped that good will from New Zealand's participation in the Korean War in the 1950s would enhance its chances.
PM has fridge full of wine but few drinking mates
Prime Minister John Key's fridge at the Hyatt in Seoul is full of New Zealand wines, but he has few visitors to consume it.
Mr Key had an informal drink with Australia's Prime Minister Julia Gillard. He said they drank New Zealand pinot noir and had "a good gossip", including an update on the Queensland election, and a discussion on how Australia's climate change legislation was progressing.
"I could have had every world leader in my room and still had plenty of booze left over. They were obviously thinking big."
Mr Key was due to meet Britain's Deputy Prime Minister Nick Clegg last night and meetings with other leaders will begin today on the sidelines of the Nuclear Security Summit.
Alas, one leader he still had not bumped into was United States President Barack Obama. Key had hoped to bump into Obama in the hotel's gym when he exercised in the early hours, but Obama was not there: "No, he didn't go to the gym. It's unlike him."
Yesterday, Mr Key went to look at the research and development hub of one of the major companies exporting to New Zealand - Samsung - and expressed some awe that their $150 billion annual turnover was the same as New Zealand's GDP.
He spent some time admiring its 3D televisions and touch screen technology - including drawing glasses and a moustache on a photo of himself displayed on one television screen. He was given a Galaxy tablet and a camera for his efforts.
