Dominic Abelen, a serving corporal in the New Zealand Defence Force, was killed last month after taking leave from army duties to join Ukraine's defence.
The 28-year-old died in Ukraine's eastern region under heavy Russian gunfire, and his body has not been recovered.
Ron Mark, a former soldier who served as defence minister from 2017 to 2020, told Radio NZ he estimated about 20 Kiwis were fighting as part of an international legion.
Mr Mark believes more could soon follow.
"Yes it's an emotional response and yes there's a desire for revenge," he said.
"A guy that they respected, knew and loved has just been killed over there.
"From the feedback I'm getting, the number of interested enquiries has ballooned quite considerably."
Mr Mark said efforts to recover Mr Abelen's body were complicated by his nationality, and abandoned due to risk.
"Dom would not have wanted someone to die trying to recover his dead body and they knew that. But they tried," he said.
"So long as Dom was just another body on the battlefield, to the Russians, then there was a chance that he was just going to be left there.
"The moment it became public ... that he was a serving infantry soldier in the New Zealand army, clearly was going to become of political interest to the Russians to get his body as quickly as they could and hold it."
In the wake of Mr Abelen's death, both Ms Ardern and the New Zealand Defence Force cautioned other Kiwis against travelling to Ukraine.
Still, some soldiers have joined the fighting ranks, while others - such as Mr Mark and former Tauranga Mayor Tenby Powell - have travelled to provide humanitarian or logistical support.
Last week, Defence Minister Peeni Henare told AAP an audit of soldiers currently on leave without pay was yet to find any other serving Kiwis in Ukraine.
On Monday, Ms Ardern said six Kiwis had lodged their details with the foreign ministry's SafeTravel registry.
She said she was unaware of any serving soldiers who had travelled, or any who had resigned to take up arms.
Like Australia, New Zealand is supporting Ukraine's defence in several ways without sending soldiers to the front lines, including financial and military aid.
The NZDF has deployed 120 soldiers to the United Kingdom where it is currently training Ukrainian fighters.
Ms Ardern refused a suggestion from Mr Mark to set up an embassy in Kyiv, believing it would incentivise New Zealanders to travel to Ukraine.
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