The Canadian speakers were due to speak at Takapuna's Bruce Mason Centre next week but faced strong criticism from the council.
Yesterday the coalition said in a memorandum that the application for urgent interim orders was no longer being pursued.
But the group said it still wants a hearing in a month, after having further discussions with Auckland Mayor Phil Goff and the council, when the pleadings may also be refined.
Goff told the Herald yesterday he believed the coalition's basis for a court hearing were weak and he was not surprised by the outcome.
"I'm obviously pleased that they've withdrawn their action, it was always based on grounds that were incorrect, ill-conceived, and their case was weak.
"They've been backing away from it for days now ... I'm not surprised they made that decision," he said.
The group raised around $90,000 to challenge the cancellation and the role they believed Goff played.
The mayor believed even if the talks had gone forward, New Zealanders would not be interested in hearing what Southern and Molyneux had to say.
"I doubt they would have had much of an audience anyway to pay $79 to hear somebody describe Hitler as a social justice warrior.
"While they might have the freedom of speech to come here, they don't have the automatic right to a venue that is funded by some of the very people they were setting out to abuse and insult," he said.