The Australian Maritime Union is warning Maersk Shipping and other companies that they risk action if they continue to offload at the Ports of Auckland, during the strikes.
The company and the New Zealand Maritime Union are in mediation again on Friday as union members enter week two of a four week strike.
The port says only two ships, Maersk Aberdeen and Irenes Remedy, have docked and unloaded so far.
But Maritime Union of Australia assistant secretary Will Tracey says that's wrong and the Maersk ships face trouble at ports across the Tasman. He says they should not risk escalating the situation.
Mr Tracey says the union will provide every level of assistance to the New Zealand union members in terms of an industrial campaign.
Maersk Shipping would not comment.
Mediation progress claimed
The Maritime Union is hopeful the talks will end the stalemate.
President Garry Parsloe said on Friday morning that he was more hopeful of making progress than before.
Mr Parsloe said both parties were bargaining in Thursday's talks; something, he said, that had not been achieved in the past.