The two sides in the bitter industrial dispute on the Auckland wharves begin a fourth round of mediation today with little sign of a solution in sight.

Ports of Auckland boss Tony Gibson yesterday said he was not prepared to budge from the company's final offer to the union and has begun steps to lay off 330 union workers.

Today's mediation follows a fifth port strike, which ended at 11pm yesterday. Workers have also been locked out by the company for 48 hours during the industrial stoush, which started on December 2.

Mr Gibson said he had reached the end of his tether after months of formal and informal talks.

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"We have got to move on. The board is resolute. The management team is resolute. We need and have to have the right to manage the terminal so we are actively and urgently pursuing the consultation around contracting out," he said.

The process of contracting out includes distributing a formal "request for proposal" document to five private companies this week to replace the union workforce.

Mr Gibson said the company was still prepared to listen to innovative solutions to work practices from the union.

The port company's final offer last week of increasing hourly rates by 10 per cent in return for replacing eight-hour duties with shifts ranging from five to 12 hours was met with a counter-offer by the union of a 2.5 per cent increase and rolling over the existing contract for six months to investigate ways to boost productivity.

The port company has refused to say what its offer would mean for labour costs at the port, except that its staff hours per container were about 1.21 hours and it would like to reduce that figure to less than 1 hour.

Mr Gibson said the counter-offer fell well short of what was needed to improve work practices and productivity.

Maritime Union president Garry Parsloe said the union was entering mediation to mediate, but Mr Gibson was going in with a take-it-or-leave-it position.

"We hope he can be a little bit more conciliatory because we intend to be. We are saying we have had the strikes, the stoppages, the lockouts and all the yelling and screaming.

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"It is now in the interest of the port and the people of Auckland that we sit back and try and listen to each other and come up with a compromise ... that both parties can live with," Mr Parsloe said.

He said the union had tweaked its offer in areas such as a roster system to come closer to what Mr Gibson wanted.

A senior source at the Auckland Council, which owns 100 per cent of the port company, said it was a critical week for the dispute.

Leah Thornton yesterday took her four children, Nina, 4, twins Amy and Max, 5, and Ben, 9, down to support their father at the picket line.

"This is not just about the guys, this is about the union. And this is a family issue, it affects everybody," she said.

Mrs Thornton and her children, among other workers' families, took turns holding the signs which read: "All my Daddy wants is a roster".