Abelen died fighting Russian forces while on leave without pay and was not on active duty.
"Unfortunately, of course, it is a war zone that he has been lost in," she told TVNZ's Breakfast show.
"So we are very constrained in this environment - either getting good information, but also in being able to provide assistance on the ground."
She said there is no consular support on the ground - the nearest being in Warsaw, Poland, which is about a 13-hour drive away.
There are also no foreign armies or partners that New Zealand would otherwise normally work with - none of whom are present in Ukraine.

Ardern said authorities are trying to glean additional information on the ground. However, she acknowledged that it was very hard to understand how accurate that information is.
"But what information we have, we're sharing directly with the family rather than putting into the public domain."
Ardern said she has received more information than what has been publicly shared, and reassured that Abelen's family is aware of all the details that she has.
Speaking to AM, Ardern said the reasons for not sharing more with the public was due to privacy and security issues.
She said the information they are receiving has been difficult to confirm.
"[There are] high levels of uncertainty because of course it's a war zone," she said.
Ardern said she does expect to receive support from the Russian Embassy in New Zealand.
"Obviously this is a war that is unprovoked and unjustified at the hands of Russia so, as you can imagine, you would have seen from their treatment of other foreign nationals, that this is not an area at all that I would expect them to be supportive," she said.
Asked by RNZ if Abelen's body was in the arms of Russia, Ardern couldn't confirm.

"The issue is are we even going to have the ability?" she told RNZ.
Of 94 defence force staff currently on leave without pay, Ardern said the NZDF was not aware of any of them being in Ukraine.
"Of course, if you're on leave without pay, the expectation is that you not be in Ukraine," said Ardern.
Corporal Abelen had not been given permission to enter Ukraine and he had not told them about his plans, the NZDF said in a statement.
"It is not known how many NZDF personnel on leave without pay may be in Ukraine. No personnel have been approved by NZDF to enter the country," the statement said.
It declined to say whether it was checking the whereabouts of all its soldiers on leave, including those on leave without pay.
Ex-soldier and former mayor of Tauranga Tenby Powell is in Ukraine providing humanitarian aid and helping with the evacuation of civilians.
He was working closely with the Defence Force to bring back the body, he has said.










