The mayor was responding to a media release from ACIL and the ports company that said discussions on the extensions to Bledisloe Wharf could continue over "coming weeks".
ACIL chief executive Gary Swift said: "We understand the mayor's concern, and indeed are working as hard as we can to resolve the matter as quickly as possible."
Last week, council chief executive Stephen Town asked ACIL to "encourage" ports bosses to halt extensions until the study was done. The boards of ACIL and the ports met on Thursday.
In a ACIL letter to the ports, Mr Swift expressed concern that the ports company believed an engagement programme with key stakeholders would not affect the timing of contract works for the wharf extensions.
"The ACIL board expects that the Ports of Auckland board has made its decision in relation to this work with due regard to the economic and financial interests of the company, its shareholder and the people of Auckland.
He said ACIL had no legal power to direct the port board but strongly suggested no further physical works be undertaken on the wharf extensions until the study was done.
Enabling works have started on the extensions. A ports spokesman said main works could start this month or next month.