Prime Minister Jacinda Ardern says a completed free trade deal with the EU by the end of this year is realistic, but New Zealand will still push hard for open access for agricultural products to the EU market.

A deal with the EU is estimated to benefit New Zealand by as much as $2 billion a year, and promoting it has been a central focus of Ardern's trip to Europe this week.

Late last night (NZT) Ardern met European Council President Donald Tusk and then European Commission President Jean-Claude Juncker, who expressed a strong desire to finish the deal as soon as possible.

"We should do everything possible to conclude the trade agreement between New Zealand the EU in the course of this year," Juncker said at a press conference after his meeting with Ardern.

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"I'm convinced, given the good spirit that did impact our discussions today, that this is possible. New Zealand is far on the map, but close to our hearts."

Just before boarding a flight back to New Zealand this morning, Ardern said she was pleasantly surprised at the level of enthusiasm for a swift solution.

"The degree with which he [Juncker] was putting emphasis on that really stood out to me and surprised me. He shared that ambition publicly. He wants to see the deal done.

"There are benefits to us concluding and moving quickly, but at the same time we need to make sure it is a quality deal.

"Things are moving quickly, keeping in mind that New Zealand's starting point is basically open access to the EU. That probably is in part why this is a negotiation they believe they can move quite quickly on."

Agriculture remains a sensitive issue, and European Commissioner for Agriculture and Rural Development Phil Hogan will visit New Zealand in two weeks.

Ardern said New Zealand's agricultural produce was in high demand, but they were already in the EU markets and often had points of difference.

Earlier this morning, in an interview with Politico Europe, Ardern made the point that New Zealand could only produce so much of the world's food supply.

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"As much as people think that we are 100 per cent populated by sheep, we are not," she quipped during the interview.

"This is a market where we can coexist. And you export stuff to us too. You've just been able to do it a little more freely and openly than we have."

An FTA with the EU has been estimated to boost New Zealand's annual GDP by $2 billion and increase exports by up to 20 per cent.

Current tariffs include 22 per cent on tuna, 8.8 per cent on kiwifruit, and 12.8 per cent on tomatoes.

Besides the US, the EU is the largest trading partner that New Zealand does not have an FTA with. In 2017, New Zealand exports to the EU added up to $5.2 billion, while imports from the EU totalled about $10.7 billion.