He said National's Korean MP, Melissa Lee - who is also on the trip in Seoul - would talk to other South Korean MPs to try to gather their support.
"We acknowledge there is a domestic lobby that's opposed and these things always take some time. It took six years to negotiate the free trade agreement with the United States so it's clear that domestic pressure was there."
He said President Lee had raised that issue "but he's strongly of the view that there are benefits for both countries, that New Zealand is a significant trading partner".
President Lee had acknowledged that without a free trade agreement, New Zealand companies were at a significant disadvantage to those from Europe and the United States because of hefty tariffs, he said.
"The challenge isn't just to maintain our market share, but, bluntly, Fonterra and Zespri are really up against it when they're competing with countries that have either no tariffs now or very low ones."
At the moment South Korea is New Zealand's fifth-largest trading partner - New Zealand exported goods to the value of $1.7 billion last year, predominantly timber, aluminium, dairy and meat. However, there are also valuable niche markets.
It is New Zealand's biggest market for deer velvet (worth about $25 million a year) and its second-biggest market for green lipped mussels ($23 million). In return, New Zealand imports cars and electronic goods.
Mr Key had tried to keep the trade talks going on his last visit to Seoul in mid-2010. However, they have been stalled since then after South Korea, with domestic sensitivities about free trade deals, asked for a hiatus to allow it to complete its deals with Europe and the US. The United States deal came into effect last week.
Australia's talks have resumed but have reached an impasse over South Korea's request for an investor disputes clause, which would allow its companies to sue companies from the other country.
Tomorrow Mr Key will visit the Samsung headquarters in Seoul for a sneak peek at upcoming technology. The Nuclear Security Summit will open this afternoon and begin with a working dinner for the leaders.
On the sidelines, the issue of North Korea is expected to be high on the agenda. Neither North Korea nor Iran are at the summit despite global concerns about their capacity for making nuclear weapons. North Korea has voiced discontent about the summit and released plans for a missile launch which it says is aimed at putting a satellite into space. Most other nations - including New Zealand - have condemned it.
One of Mr Key's bilateral meetings has fallen through - the Netherlands' Prime Minister opted to stay home to try to resolve problems within his coalition government. However, Mr Key will meet British Deputy Prime Minister Nick Clegg for the first time.
He is also due to hold talks with Thailand's Prime Minister, Yingluck Shinawatra, Canadian Prime Minister Stephen Harper, President Sebastian Pinera of Chile and Vietnamese Prime Minister Nguyen Tan Dung. Chile and Vietnam are among the nine Asia Pacific countries involved in negotiations for the Trans-Pacific Partnership trade deal and Mr Key said that would form part of their talks.
