That follows a last-minute decision by a Singapore-based shipping line to turn around a container vessel and its cargo including foodstuffs and industrial supplies in the Hauraki Gulf on Sunday night and divert it to Tauranga, under alleged union pressure.
Auckland port company chief Tony Gibson and the union, whose members are striking against a threat to contract out their jobs, traded claims and denials yesterday about where such pressure came from.
Mr Gibson said Ports of Auckland was urgently considering whether it could sue the union for damages.
He said it had been told by the shipping company Pacific International Lines of being threatened by a Maritime Union official from a conference in Australia with a "black ban", a claim denied by union president Garry Parsloe.
"I am the spokesman for the Maritime Union of New Zealand and I never said it and never instructed anybody to say it," he said.
"International unions talk to international shipping companies every day - they are entitled to do that - nobody can stop them and if that results in ships not coming to Auckland, I can't do anything about that."
Importers' Institute secretary Daniel Silva, although a strong critic of the strike, said the company was "barking up the wrong tree" by investigating legal action against unionists.
"They are in the business of demanding with menaces, and the law allows it," he said.
Despite his pessimism, both sides have agreed to meet before a mediator on Thursday and Friday to explore the chance of settling a new collective employment deal.