The head of the Accident Compensation Corporation says it will consider each case of sensitive claimants whose private details were released to see whether further compensation is required.
The corporation offered in June to pay $250 to each of 200 claimants in compensation for mistakenly emailing their information to another claimant, Bronwyn Pullar.
A lawyer specialising in ACC matters, John Miller, says the offer is insulting and he intends to take action on behalf of about 100 of the claimants.
Another lawyer, Hazel Armstrong, has warned that those who seek greater damages may face a costly battle.
Ms Armstrong says they will have to prove they've suffered emotional harm because of the privacy breach.
"Possibly depending on how far ACC pushes it, they might have to show a level of significance that would have to be measured by a psychiatrist, and a psychiatrist's report can cost anything between $2000 and $7000."
ACC chief executive Ralph Stewart told Radio New Zealand's Morning Report programme the $250 offered is to recognise that the corporation had made a mistake.
"If the individual concerned is not happy we want to talk to them here about that and consider their own individual position."
Claimants not satisfied with this process have the option of going to the Office of the Privacy Commissioner or the Human Rights Tribunal.
Mr Miller is confident the case is strong and says his firm will take action on a pro bono basis.
He says he will go to the Human Rights Tribunal only if negotiations with ACC and the Privacy Commissioner fail.