New Zealand Prime Minister John Key said before the election that encouraging free trade for New Zealand's goods gave the country access to big international markets, and the conclusion of a Korean FTA was close.
South Korea is New Zealand's fifth-largest trading partner, with total trade last year worth $3.59 billion, according to MFAT.
It is the country's fourth-largest source of foreign students and seventh-largest source of overseas visitors.
New Zealand exporters pay about $229 million in Korean tariffs each year, and the talks begun in 2009 have previously stalled amid Korean concern about the impact of New Zealand agricultural exports, says MFAT.
Australia and Canada, who both compete with New Zealand to export agricultural products to Korea, have recently concluded FTAs with Seoul.
Tariff elimination on agricultural products remains a challenge with New Zealand arguing that it doesn't compete with sensitive Korean production.