Unionised cargo workers refused to handle the Maersk Aberdeen when it came into port on Friday because it had been worked by non-unionised labour in Auckland.
About 60 people picketed the port on Saturday night during stormy conditions and another smaller picket was forming outside the port's gates today.
Centreport said all other vessels were being handled, and it was seeking a court injunction tomorrow to force the workers to handle the ship.
It was working through a backlog of ships that had developed due to the weekend's bad weather.
Mike Clark, secretary of the Wellington branch of the Maritime Union, said cargo workers were being asked one by one by the company to comply.
Union members said their protest was peaceful, although it was unclear whether they would block incoming cargo for the Aberdeen.
"We're trying to avoid disciplinary action of our members,'' Mr Clark said.
A similar scene occured in Tauranga during the weekend when members of the Rail and Maritime Transport Union refused to unload another "blacked'' ship. The ship was delayed for two days.
Joe Fleetwood, the Maritime Union's general secretary, was at the port and said he hoped the action would not drag on, but the company had laid down the law this morning.
"[Between] 330 to 350 of our members are being treated with disrespect and everyone in New Zealand deserves to be treated with respect and dignity in the workplace.''
The Aberdeen had also broken its agreement with the International Transport Workers Federation to only use ITF-approved union workers, he said.
Mr Fleetwood said the agreement could spill over to other centres, as the ship was due to visit Lyttelton and Nelson before leaving for Australia.
"I can't confirm what will happen when it leaves Wellington.''
Mr Clark said it was the first time there had been union action at Centreport in a long time.
"It has been quite amicable but there's two sides to the story too.''
The port had an obligation to look after its customers but workers had an obligation to their colleagues in Auckland, he said.
Unionists claim the Port of Auckland action is getting international attention, and there would be union delegates from America and Australia at a rally in Queen St on March 10.
Centreport has 200 staff, most of them members of one of five unions.