The Ports of Auckland says it is in talks with Mayor Len Brown and opponents of its planned wharf extensions, and it has not ruled out delaying construction, which is due to start next month.
During the weekend, Mr Brown said he wanted some "latitude" around the start time of the building work.
In a statement, the Ports of Auckland said it would wait and see what the outcome of discussions were before making any decision on whether or not to pause construction of the extensions.
Pressure group Urban Auckland said it would press ahead and file legal papers against the port company on Thursday, arguing the resource consents for the Bledisloe Wharf extensions were granted unlawfully.