The Maritime Union is meeting Ports of Auckland on Monday before further mediation talks are held on Tuesday.
The wharves have been closed for nearly four days because of strikes and lockouts after the parties failed to agree on the terms of a new Collective Agreement
The latest strike, which involves more than 300 Maritime Union members, ends on Monday night, but will resume next weekend if no deal is reached.
Maritime Union president Garry Parsloe says the union wants the issue resolved as quickly as possible.
Denial issued by union
Earlier, the union said one of its officials categorically denies inciting members to use force to stop non-members from working during a strike.
The Ports of Auckland made the accusation. It says police are investigating the official after he was issued with a trespass notice for two years.
About 300 members of the union are on a 24 hour strike until Monday evening.
Mr Parsloe says there has been no violence during the strike.
