"RSD has no intention of hosting any live events in New Zealand," it tweeted. "All events have been canceled [sic]."
It had initially advertised a seminar set down to take place in April this year.
Numerous Australian media outlets have reported one of its members, Jeff Allen, put an end to his Australian tour after the Government there cancelled his visa.
In 2014 another of its members Julien Blanc faced similar controversy and also had his visa cancelled on his Australian tour.
Immigration New Zealand said yesterday even if Mr Blanc made it to the New Zealand border he could be stopped from entry as a result of having been deported from Australia.
Section 15 of the Immigration Act provides that anyone who has been deported from another country cannot be granted entry to New Zealand except by a special direction from the Immigration Minister.
Women's Refuge has responded to the news on its Facebook page with a thumbs up.