The members said they supported the company's operational independence but the dispute had "escalated to a strategic level".
"We are particularly concerned that actions being taken by Port management, including what appears to be a pre-determined strategy to contract out port jobs, are inflaming matters," the members said.
"... We recognise the need for competitive levels of operational efficiency at the port. But Port management's proposal to fire a skilled workforce and contract out their jobs to an external provider, with few work-life balance protections for employees and their families, is not the best way to achieve this."
The members also expressed concern the dispute was being used as a "wedge" by some councillors and interest groups to promote privatisation.
"We support Mayor Len Brown's unequivocal pro-public ownership platform, and believe the Port CEO would be well advised to publicly support it too."