Mr Parsloe is currently in Australia attending two union conferences, and will be addressing leaders of the International Transport Federation this morning before returning to Auckland.
Before Mr Parsloe left he told the Herald shipping companies which docked at the port's Fergusson container terminal "won't be welcome anywhere else in the world".
He cited a case about 12 years ago when a ship loaded by non-union labour was turned back to Melbourne by unionists in Los Angeles.
Port company chief executive Tony Gibson responded by saying the union was "inciting international third parties to act against the interests of Auckland".
Yesterday, Mr Parsloe said the website ads demonstrated Mr Gibson's "staggering hypocrisy".
"We can't talk to Australians, but he can hire them to replace his own workers ... why would we be in there negotiating for a collective employment agreement, while our jobs are being advertised all over Australia?"
Mr Parsloe called on Auckland Council, which owns 100 per cent of the port, to dismiss the port's senior management.
"This is a rogue management with its own agenda and the council must step in to protect the interests of Auckland."