New World Centre City owner Craig Nieper said when contacted the store was engaged in good-faith bargaining and would not comment.
"I am unwilling to carry out this process in the public arena as I do not believe it fits with the good faith process," Mr Nieper said.
First Union organiser Bill Bradford, of Auckland, said Foodstuffs South Island staff were paid up to $2 less an hour than Foodstuffs North Island staff.
Mr Bradford said many South Island staff earned the minimum wage or not much more, including long-serving staff. In April, the minimum wage would increase by 50c to $15.75 per hour.
Mr Bradford acknowledged there was no official South Island pay rate, but said the South Island co-operative offered uniform rates across its stores, as did the North Island entity. Foodstuffs, which operates New World and Pak’n Save, has separate South Island and North Island co-operatives.