"But the aspect that is of the greatest concern is that very significant numbers of them are being sent off to Christmas Island, and that means they are isolated from family and friends and, most importantly, their legal advisers."
Around 200 New Zealanders are being held in seven detention centres awaiting deportation, after Australia toughened its rules to deport criminals, some who had not lived in New Zealand for many years.
Professor Triggs, who has been attacked by the Australian Government over her criticisms of detention centres, is seeking a meeting with Immigration Minister Peter Dutton to discuss the issue.
She last visited Christmas Island a year ago and described conditions there as "inhumane, dangerous and extremely poor".
Professor Triggs said she did not think New Zealanders were being especially targeted.
"New Zealanders have just got caught up in this net that has been cast over the whole of Australia."
Togatuki, 23, who had mental health illnesses, died in solitary confinement in Goulburn's Supermax prison in Sydney. His sentence for robbery and assault had ended in August, but he was being held ahead of his deportation to New Zealand - the country he had left aged 4.
Prime Minister John Key, who is in New York for the United Nations General Assembly, said he wanted to raise the wider issue of deportations with Malcolm Turnbull, but the timing for that would not be immediate as the new Australian Prime Minister was not in the US.
Labour's foreign affairs spokesman David Shearer said the party had wider concerns about the treatment of Kiwis in Australia, including a lack of entitlement to benefits.
While Mr McCully was meeting Ms Bishop about Togatuki's death, Mr Shearer said there was a lack of urgency over the broader deportation issue.
That, he said, showed the relationship was not as special as the Government claimed.
Kiwis in custody
• Since last November the Australian Government can deport non-citizens who had been jailed for at least a year.
• There are close to 200 New Zealanders in Australian detention centres, including on isolated Christmas Island.