Consular support from Warsaw was being offered, she said.
Asked about the circumstances of Abelen's death, Henare said "we know very little" and work was being done with both his and Mahuta's agencies to work out what happened
"The job now is to find out more details. The entire situation is a complicated one," Henare said.
Henare was advised that no NZDF people on leave would be travelling to Ukraine and that option was banned by the defence force.
He said it would be difficult to check in with all members on leave without pay as to whether they are in Ukraine or not as there were no set check-in requirements.
He wouldn't comment on the decision-making on why Abelen went to Ukraine.
He said the focus now was to regenerate the defence force workforce
Mahuta said Abelen was someone who was on leave and not representing New Zealand or the defence force.
She said on the basis of Abelen's travel, work would be done through the Ukraine Government and his family to try and bring him home.
Asked whether the defence force will check in with everyone that was on leave without pay, Henare again said that wasn't a straightforward process but he did say he would support that if the defence force thought it was necessary.
He had not directed them to do so though.
Mahuta was clear the travel advisory was not to go to Ukraine. Decisions to go there were made by the people themselves.
"We will miss you brother. So much. You have left a hole that we are feeling and we could never hope to ever fill."
He called him a "warrior until the end".
Others have spoken of their shock at losing a "solid operator" and a brother of the famed 2nd/1st battalion.
Defence Minister Peeni Henare expressed his condolences to the family, friends and colleagues of the Kiwi soldier.
"I have been advised the New Zealand Army are supporting the soldier's family through this difficult time," he said.
I express my condolences to the family, friends and colleagues of the NZ soldier who is reported to have died in Ukraine while on leave from the Army. I’ve been advised the NZ Army are supporting the soldiers family through this difficult time. https://t.co/NAjZV9MXzw
Former soldier and No Duff Charitable Trust co-founder Aaron Wood today said it was only a matter of time before a New Zealander was killed in the fierce fighting.
"If anything, it's surprising it hasn't happened sooner, and more often," said Wood who likened the fighting there to "every bad nightmare story that came out of the eastern front circa 1944/45".
"When people engage in that, you're counting the days," he said.
"While it is obviously very sad that he was killed, he knew what he was doing. I don't mean to sound cliched or callous, it's more of a pragmatic approach.
"He would've known the risks and had been there a while... and quickly figured out whether or not it was for him … and the fact that he stayed, he was comfortable with it."
Former New Zealand Defence commanding officer Tenby Powell, who is in Ukraine undertaking humanitarian work, said he had been asked by the family of the dead soldier to bring the body back to New Zealand.
While he was not willing to go into details about the circumstances of the soldier's death he told Today FM the family were distraught.
"It's a very sad day here in Ukraine, not just for New Zealanders but for everyone."
August is always a tough month for many serving and former members of the Defence Force.
The "Battle of Baghak", a Taliban ambush near Dahane Baghak in the Shikari Valley of Bamyan Province on August 4, 2012, was New Zealand's bloodiest battle since Vietnam.
Lance Corporals Rory Patrick Malone and Pralli Durrer, both aged 26, were killed in the fierce shoot-out north of their Kiwi base, while six comrades were wounded.
Two weeks later, on August 19, 2012, Crib 20 deployment comrades Corporal Luke Tamatea, 31, Lance Corporal Jacinda Baker, 26, and Private Richard Harris, 21, died when their Humvee hit a 20kg roadside improvised explosive device.
Lieutenant Tim O'Donnell was first of 10 Kiwis killed in Afghanistan, when on August 3, 2010, while serving as part of New Zealand's provincial reconstruction team in Bamiyan province in Afghanistan, he was killed in an attack.
SAS soldier corporal Douglas "Duggy" Grant died in a firefight with Taliban insurgents as he tried to rescue civilians following an attack on the British Council building in Kabul on August 19, 2011.