Port protesters are targeting Mayor Len Brown to stop work on two huge wharf extensions into the Waitemata Harbour.
The Stop Stealing Our Harbour group plans a public rally on May 3 at a location still to be confirmed.
The group's first rally at the end of Queens Wharf on March 22 drew about 2000 people. About 300 boats took to the harbour in support.
The latest rally follows confirmation from Ports of Auckland that work is proceeding on the extensions at the end of Bledisloe Wharf.
Stop Stealing Our Harbour spokesman Michael Goldwater said Mr Brown needed to enforce what the council had asked the council-owned port to do - stop work.
"The ports are using brinkmanship to try and get their way and bullying the rest of Auckland to having more concrete in the harbour," he said.
A statement from the mayoral office said the council was monitoring the situation daily while it waited for a response from the ports company on stopping work.
It said Mr Brown expected a response soon and he could call an extraordinary meeting to discuss whether the ports company had adequately addressed council concerns.
Mr Goldwater and Whau councillor Ross Clow yesterday separately called for the ports company to demolish Marsden Wharf to the west of Bledisloe Wharf as a temporary solution to accommodating bigger ships.
Mr Clow said this would allow the Bledisloe extensions to be delayed while an extensive port study is done.
Mr Goldwater said demolishing Marsden Wharf would easily accommodate the 345m long Queen Mary II cruise ship.
The port company has begun demolishing the northern piled section of Marsden Wharf, but ports spokesman Matt Ball said it would have to remove the entire wharf, dredge the basin, build a new seawall and strengthen the southern end of Bledisloe to take larger ships.
"We do not have consent for any of the other works," he said.
Public notification would be needed to declaim the southern reclaimed section of Marsden Wharf, "so it won't be a quick process".
Meanwhile, Simon Allen, who chairs the council body overseeing the ports company - Auckland Council Investments Ltd - and deputy chairwoman Miriam Dean, QC, will step down from the board this year.
Mr Allen, who has chaired the board since 2010, said he gave the council notice 18 months ago.
It had nothing to do with the port issue, he said.
• Second protest planned for May 3
• Time and location still to be finalised
• Protest is response to work proceeding on wharf extensions