Wellington's Centreport is to go to the Employment Court in a bid to force workers to load and unload a ship recently arrived from Auckland.
Unionised port workers in Wellington are refusing to handle the Maersk Aberdeen because it was processed by non-unionised workers in Auckland.
More than 300 members of the Maritime Union are taking strike action for four weeks as they try to negotiate a new collective agreement with Ports of Auckland.
The standoff in Wellington began on Friday night when about 60 mainly union members picketed at Centreport to coincide with the arrival of the ship.
Centreport's chief executive Blair O'Keeffe says talks with the Maritime Union on Monday failed to resolve the standoff and the matter will go to court on Tuesday.
Mr O'Keeffe says his staff are legally obliged to fulfil the conditions of their collective employment agreement.
Centreport is acting reasonably and responsibly to resolve a situation that is not of its own making, he says.
Maersk Line's country manager, Julian Bevis, says it's difficult to gauge just how disruptive the industrial action has been, and to put an exact figure on the costs.
However he said there had been additional costs for the company in taking operational measures to cope with cargo delays and a cost to its customers whose stock may not arrive on time.
Up to 30 port workers picketed at the Port of Tauranga when they were asked to work on Irenes Remedy, another Maersk ship processed in Auckland by non-union workers, but an injunction from the Employment Court has since forced them back to work.
The Shippers' Council is concerned that the industrial action which started at the Ports of Auckland may spread internationally.
Chairman Greg Steed told Morning Report that international union leaders who have arrived in New Zealand are suggesting there is international support, which would up the ante.
He says the industrial action in Auckland has gone on so long that even big companies used to coping with different forms of disruption are starting to feel the effects.