"I think we're getting very close to a successful conclusion of a free trade agreement," Key, who is on a Gulf tour, told a reception at the New Zealand embassy after meeting King Salman.
Key is the first prime minister from his country, a non-permanent member of the United Nations Security Council, to visit Saudi Arabia.
Trade Minister Tim Groser told reporters there were no major obstacles to concluding the free trade deal.
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"The negotiation with New Zealand is complete," and legal experts just need to review the texts before "we can proceed," he said.
New Zealand is the world's largest exporter of dairy products and sheep meat, and is one of the largest exporters of halal food, Groser said.
Given that the Gulf states including Saudi Arabia import about 90 percent of their food, "we are an important part of the food security" of the region, he said.
Two-way trade between New Zealand and Saudi Arabia totals about $1.5 billion, "but we see enormous potential for growth here in the next 10 to 20 years," Groser said, adding that the Gulf states are "an ocean of stability in a very difficult region."