New Zealand is grappling with how best to support the family of Corporal Dominic Abelen, the 28-year-old soldier who was killed after travelling to the war against defence force rules.
Mr Abelen was on leave without pay and travelled to Europe without telling his family or the New Zealand Defence Force (NZDF), which forbids soldiers joining the band of unsanctioned foreign fighters taking up arms against Russia.
The prime minister said she had "only sympathy and condolences" for Mr Abelen's family, whose death has raised tricky questions for her government.
New Zealand has offered financial, military and logistical aid towards Ukraine's defence, while slapping financial and travel sanctions on key supporters of Russia's regime.
However, like all of Ukraine's supporters, New Zealand has not joined the war by putting boots on the ground.
While there are calls to bring Mr Abelen's body home, Foreign Minister Nanaia Mahuta has stressed New Zealand is treating the case of Mr Abelen as that of a citizen rather than a soldier.
Ms Ardern said it was difficult for New Zealand to do anything about Mr Abelen at present.
"The issue is whether or not we're even going to have that ability (to access Ukraine) ... it is a war zone," the prime minister said.
"We do not have people on the ground. We do not have consular support on the ground.
"It's very difficult for us to to do much at this present point in time. That does not mean however that we are not seeking as much information as possible and trying to understand the circumstances."
In radio and media appearances on Monday morning, Ms Ardern declined to answer a string of questions around the matter, including where Mr Abelen died, where his body is, whether they know where the body is, and if it is in Russian hands.
Kiwi media reports suggest Mr Abelen died while attempting to re-take a series of trenches in the eastern Donbas region.
Ms Ardern did say Mr Abelen's family were being briefed, saying "they have as much information as we have".
It is not clear how many other New Zealanders have joined Mr Abelen in volunteer battalions, as urged by Ukrainian President Volodymyr Zelenskyy.
The NZDF reports 94 personnel currently on leave without pay, and Ms Ardern said army chiefs were "going through an outreach process" to see whether others were in Ukraine.
Ms Ardern said her advice to anyone looking to travel to Ukraine - soldiers, humanitarian workers or otherwise - was to forget about it.
"There's a reason why New Zealand has has made very clear that Ukraine is one of those areas where the advice is do not travel," she said.
"We give that advice when we know that we're unable to provide support on the ground.
"We cannot assist and it is always our preference that if New Zealanders need us, that we can get them out."
The Labour leader said attempts to secure consular support through the Russian ambassador was unlikely to prove fruitful.
"I would not have an expectation of any great degree of assistance. This is a war which is unprovoked and unjustified at the hands of Russia," she said.
Mr Abelen spent a decade in the army, serving with the 2nd/1st Battalion Royal New Zealand Infantry Regiment based in Burnham, outside Christchurch.
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