Mark John Taylor, also known as Mohammad Daniel and Abu Abdul Rahman, made the comments in a YouTube video.
The broadcast was removed after being viewed only a handful of times, but footage played on TV3 News showed Taylor addressing supporters in New Zealand and Australia.
"Now is the time to commence your operations. Even if it means you have to stab a few police officers or soldiers on Anzac Day, so be it."
Taylor said Isis sympathisers whose passports were confiscated by authorities to stop them travelling to fight in the Middle East should carry out operations here and in Australia.
Asked about the video, Prime Minister John Key said it showed that Isis were trying to bring their war to New Zealand. He said a number of people would be under close watch by New Zealand security agents.
"We will be watching those and continue to watch those people very closely," he told TV3.
Taylor was nicknamed the "bumbling jihadist" by media after he mistakenly broadcast his exact location after forgetting to turn off a tracking function on his phone.
Taylor deleted 45 posts from Twitter late last year after discovering that he had been revealing his location to intelligence agencies and enemies keeping tabs on him.
The tweets apparently show that in October he was with Isis in Kafar Roma, an area that President Bashar al-Assad's Syrian Army has previously confirmed had been occupied by pockets of foreign fighters from Isis.
Earlier and while in war-ravaged Aleppo, Taylor claimed to have been in touch with the New Zealand Government in a bid to get a new passport after burning his last one.
He travelled to see John in Yemen in 2009, leading to him being recommended for travel restrictions.
The same year Taylor was arrested by Pakistan authorities while trying to gain access to an al-Qaeda and Taleban stronghold close to the Afghanistan border and was subsequently subjected to travel restrictions by the New Zealand Government.
He left New Zealand again in May 2012 and worked in Indonesia for two years as an English teacher. In June last year, he entered Syria across the Turkish border "as a soldier for Allah".
In a statement, police said they were aware of the video.
"The identity of this individual is well known to New Zealand authorities, and he has previously sought publicity to air his views.
Police and its security partners have conducted a thorough assessment of the video.
"We take our responsibility for the safety and security of New Zealanders very seriously and, while we are unable to go into detail, we have already taken further security measures."
Police said they were satisfied that all appropriate and necessary measures were in place for Anzac Day.
"New Zealanders should feel confident in attending Anzac Day events as planned, while exercising their usual vigilance in light of the current global security environment.
"Police and its partner agencies will continue to be highly focused on ensuring the safety and security of New Zealanders is maintained, and respond appropriately to any threat which is made."
