Ardern said she hoped to meet with multiple European Union leaders, and would also meet with British PM Boris Johnson.
The PM said she hoped to discuss free trade with Johnson.
Ardern said her attendance at the Nato summit did not mean New Zealand was becoming more closely involved with the North Atlantic alliance.
"We have been, for roughly the past 10 years, a Nato partner."
The PM said New Zealand through a Nato trust fund had helped provide aid to Ukraine.
Ardern said she would continue promoting New Zealand's non-nuclear stance to Nato leaders.
She said current global instability made it imperative countries did not feel tempted to join the nuclear weapons club in misguided quests for security.
"Nuclear weapons represent a less safe world for all of us."
On additional assistance for Ukraine, Ardern said there were no announcements "here and now" to make.
Regardless of the geographic difference, New Zealand had "done our bit", she said.
It would be a protracted conflict and New Zealand was focused on seeking diplomatic solutions, and lending support in those areas too, she said.
If asked by Nato leaders for more assistance, Ardern said New Zealand was looking at the evolution of the conflict, not just looking through Nato but supporting countries surrounding Ukraine too.
"We've never said this is the end of our commitment," Ardern said when asked if New Zealand would be open to providing more assistance to Ukraine.
On former Defence Minister Ron Mark saying he will return to Ukraine, the PM said she didn't personally feel such a visit was especially wise.
"It's a war zone," she said.
Visit to Australia
After visiting Europe, the PM will visit Australia with a business delegation in Melbourne and Sydney.
She said the removal of pre-departure testing from midnight tonight would boost efforts to rekindle New Zealand's links with Australia.
On trade, Ardern said it was important for New Zealand to diversify its economy and deepen ties with the EU and the United States.
Legislation for a free trade deal with the UK will be introduced to Parliament ahead of Matariki, Ardern announced. The PM said New Zealand was also working on the closing stages of negotiations for a free trade deal with the European Union.
Earlier this month, Ardern announced she would return to Australia in July for talks between high-ranking ministers in both governments. Australian Prime Minister Anthony Albanese will also attend.
Ardern has a packed travel schedule this year, as part of New Zealand's post-Covid reconnection strategy, and she has previously said she would be travelling to Europe this year.
Also on the agenda in Europe is a long-awaited Free Trade Agreement with the European Union.
Farmers Weekly reported today that sector groups were concerned the Government would not push hard enough to ensure good market access in any FTA.
Sector leaders have flown to Brussels this week in what Farmers Weekly called a "last-ditch attempt to salvage worthwhile market access gains from trade talks with the European Union".
After a recess last week, Parliament returns to its regular sitting schedule this week.
Many ministers will have a busy week, with many scheduled to appear before select committees to answer for their budget bids in annual estimates hearings.
Speaking about controversies at Bethlehem College over gender issues, Ardern said schools in New Zealand were "obliged to ensure they have a safe and inclusive environment for children".
Some "quite serious concerns" had been raised whether that was the case, she said.
The Ministry of Education had been asked to look into the situation in greater detail and she would leave them to that job, she said.
Asked about flu season concerns, Ardern said the impacts of flu, respiratory illness and Covid-19 were coalescing to put pressure on hospitals.
Flu has overtaken Covid-19 as a source of hospitalisations for respiratory illness, the PM said.
"Please take flu seriously ... we do need more people to go and get that flu vaccine."
Ardern said face masks used to protect against Covid-19 could also help slow the spread of flu.
Ardern addressed the fuel excise duty. She said the 25c discount would continue until the start of August. But at the same time, the Government's new cost of living assistance payment to people earning under $70,000 a year would kick in.
The cost of living payment will total $350 and be paid monthly for three months to about 2.1 million people.
It was Ardern's first post-Cabinet press conference since the Tauranga byelection, which Labour's Jan Tinetti lost to National's Sam Uffindell.
Tinetti had been expected to lose the staunchly blue seat, but Ardern had been facing questions about the scale of Tinetti's defeat.
Tinetti lost by more than 6000 votes, with Uffindell posting nearly 10,931 votes to Tinetti's 4893.
"I think actually for byelections, it's very hard to read into them as someone who's run in a byelection myself because it's just simply not the same as in general elections, you don't often have every party represented, so I'm not quick to read into individual outcomes," Ardern told RNZ this morning.
