Mr Parsloe said the 330 union workers would probably not need to take strike action because the port company was probably planning to lock them out and make everyone redundant.
Mr Gibson said the company remained committed to collective bargaining while at the same time taking steps to replace union workers with private contractors.
A formal "request for proposal" document to five private companies to replace the union workforce was going out today, he said.
Mr Gibson said the union's proposals were only around the margins and did not respond to a sense of urgency for improved productivity and work practices.
"We are running out of time. Our customers are looking for a quick and definitive outcome.
"We have to protect our existing business, win back the business we have lost and put the foundations in place to achieve sustainable growth over the long term in the interests of all stakeholders," Mr Gibson said.
Mr Parsloe said the union offered to extend eight-hour shifts for one or two hours to turn around a ship without bringing on a new shift.
That was the main thing they wanted, he said, and believed the parties had a deal.
"But they went out of the room and came back in and said 'no' and I don't know what they wanted. It sounded like a lot of waffle.
"It seems like they just want to get rid of the union. We are a very strong militant union. We have large union capacity down there. They just don't want us to be any part of it," Mr Parsloe said.
Last night, the union released a "labour strategy" by the ports management, which Mr Parsloe said showed the company intended to contract out the workforce to private contractors before collective agreement negotiations began last year.
"There was never any intention to genuinely negotiate or mediate, there has just been public relations spin and an extreme anti-worker agenda," Mr Parsloe said.
A Ports spokeswoman said the document was a draft, never represented company policy, and the author had been made redundant.
Mr Gibson had been committed to collective bargaining with no pre-determined plan to contract out the union workforce, she said.