Goff said the kauri tree was a symbol of New Zealand's native forest and the council needed to do everything to ensure it survives.
The council will now consider a big funding boost in its 10-year budget to fight the disease.
Said councillor Mike Lee: "This is a formidable enemy and we don't have all the answers for dealing with it."
The committee had five management options for the forest, which include giving up the fight, maintaining the status quo, ramping up work, closing all medium and high-risk tracks, and closing the park.
Waitakere Ranges Protection Society spokesman John Edgar believed the spread would only worsen if the entire park wasn't closed.
"It's a big thing to say we're going to close the ranges, but we have to do something drastic now," said Edgar, whose group stands with The Tree Council, Forest and Bird and the Friends of Regional Parks on the issue.
Iwi executive manager Edward Ashby acknowledged there was no statutory power to enforce the rahui, but hoped people would respect it.
"The tikanga back in the old days was that when mana whenua declared a rahui, they were essentially laying down a kind of tapu, and you'd be hard-pressed to find people who would enter those areas. Of course, times change, but we didn't have many options up our sleeves."
Iwi members had set up signs around the park and Ashby said there had been anecdotal reports of just half the typical number of people seen on the tracks since Saturday.
But there were no plans to confront visitors in the park and the iwi would be taking a "softly, softly" approach.
"As mana whenua, we have an obligation as guardians, or kaitiaki, but it really falls on the council to do something.
"This is an invisible organism, it can kill a mighty kauri tree, and there's absolutely no cure at all - so the only way we can avoid this spreading is by keeping people away."