Mr Brown, a member of the Labour Party who received a $2000 donation from the Maritime Union towards his 2010 election campaign, stayed away from the protest march.
On Friday, he was the target of a lamington attack at Auckland University by an angry supporter of wharf workers, who smeared pieces of cake on the mayor's face and shirt.
Yesterday, Mr Brown said Aucklanders simply wanted their port back to full capacity and he would try everything to bring about a solution, including an offer of mediation if both parties agreed.
Mr Brown said it would be wrong to interfere before last week when the two sides were still talking, but given the importance of the port to the Auckland economy he owed it to Aucklanders to explore all options. He reiterated the need for the port, which is 100 per cent owned by the council, to double its dividend from 6 per cent to 12 per cent within five years.
But although the Maritime Union welcomed Mr Brown's offer of mediation - the Anglican and Catholic Bishops of Auckland made a similar offer on Friday - Ports of Auckland chairman Richard Pearson rejected the offer.
"We have passed the point of no return," Mr Pearson said.
He said the union workforce had been made redundant and contractors had been hired to recruit staff.
"The mayor can ensure that the workers that are striking are encouraged quickly to apply for jobs at the port and to break through the people who are bullying them not to apply for jobs," he said.
Asked if the company would accept mediation from Mr Brown if the union's application to the Employment Court to declare the contracting out of jobs as invalid succeeded, Mr Pearson said the company's legal position was "bullet proof".
PORT DISPUTE - A RECAP
* Ports of Auckland has been seeking greater flexibility and productivity on the wharves.
* Maritime Union wants a continuation of eight-hour shifts and job security.
* After months of talks, mediation, strike action and lockouts, the company sacked 292 workers, mainly stevedores, last week.
* Auckland Mayor Len Brown, whose council owns 100 per cent of the port company, has refused to take sides in the dispute.