Ardern said she pushed Nato leaders to support the deal at a dinner at the Palacio Real last night. Today in Madrid, Arden held meetings with Dutch Prime Minister Mark Rutte and German Chancellor Olaf Scholz. She pushed the trade agreement in both meetings.
Ardern said she had been speaking frequently with Trade Minister Damien O'Connor, who is in Brussels for negotiations. She said he had been updating her with the latest from the talks so that she could press leaders at the summit for more.
"We're in contact because I need to know the latest in the negotiations so I can convey that to leaders here and seek the best possible outcome for New Zealand," Ardern said.
When asked whether New Zealand's ability to negotiate was hindered by the fact it compromised on the EU's tough geographic indicator demands relatively early in the process, Ardern said that all parts of the deal remained open for negotiation.
"Everything continues to be a part of negotiations so it's not the case that one thing just gets settled," Ardern said.
Any trade deal is likely to include new rules on geographic indicators for New Zealand food producers. These would mean New Zealand producers could not label things like cheeses with their traditional European names, like camembert or gouda, as these would be protected for products that come from those regions.
The EU has proposed New Zealand change its laws to protect 2200 geographic indicators for wines, spirits and foods, meaning only EU producers could use those names.
But when asked whether New Zealand could walk away from commitments made to recognise geographic indicators, Ardern suggested the EU would be unlikely to agree to any agreement that did not include them.
"They are seeking the same thing they seek from every other FTA. The EU has not signed up to FTAs in recent times that did not include concessions on geographic indicators," Ardern said.
Ardern said the negotiations had been "complex", mainly because the areas New Zealand wants the most from, were areas where members of the EU had "sensitivities".
These areas are likely in the areas of meat and dairy.
National Party trade spokesman Todd McClay has said Arden should leave Europe without a deal if it does not offer meaningful access for agriculture.
"If real gains for meat and dairy aren't on the table, the Prime Minister should instruct negotiators to continue talks until a commercially meaningful offer is presented," he said.
He said the Government had agreed to the EU's wish to protect geographical indicators - protecting the use of words such as feta and mozzarella - giving away a big bargaining chip early in the process.
"By agreeing to geographic indicators, without reciprocal gains for meat and dairy, the Government has disadvantaged New Zealand producers and made it more difficult in our future negotiations with countries like the United States, India and the Pacific Alliance."
The Greens, by contrast, are calling on the Government and the EU to ensure any deal is comparable with both countries' climate goals and do not disadvantage small farmers.
Ardern said the argument New Zealand was making to the EU was based on the Government's climate change agenda. This is possibly mindful of the fact that Australia's negotiations with the EU had reportedly stalled because of the country's poor climate reputation.
Australian Prime Minister Anthony Albanese has said that trade negotiations between the EU and Australia were deadlocked over the previous Australian government's climate change record.
"Australia's position on climate change, where the perception by Europe and indeed by the world, that Australia was a handbrake on global action on climate change, was clearly hindering our capacity to enter into economic relationships with our European friends," he said.
Ardern said the "strong case" officials were making for New Zealand was based on the fact that the "products we are producing are some of the most sustainable practices and climate that you would see anywhere in the world.
"The EU is seeking to promote those practices," she said.
"If you can't conclude a high-quality agreement with New Zealand then who can you include a free trade agreement with?" Ardern said.