Fahrettin Altun, director of communications for the Turkish presidency, said Erdogan was in fact responding to the "manifesto" posted online by the man arrested in the mosque attacks.
"I find the comments obviously offensive, deeply offensive, but also I think very unhelpful", PM Morrison told Sydney radio 2GB on Wednesday.
"I've asked for these comments, particularly their reporting of the misrepresented position of Australia on Turkish television, the state-sponsored broadcaster, to be taken down and I expect that to occur".
Since the weekend, the Turkish leader has been using video footage of the Christchurch attack to denounce Islamophobia during campaign rallies ahead of local elections.
Ottoman Turkish troops fought soldiers from New Zealand and Australia in World War I. Now, more than a century later, a war of words has broken out over comments by Turkey's president.
"Moreover, we must shed light on all aspects of what happened and fully understand how the terrorist became radicalized and his links to terrorist groups to prevent future tragedies", Erdogan wrote.
Turkish President Recep Tayyip Erdogan has slammed Israeli Prime Minister Benjamin Netanyahu and his son for verbally attacking Turkey. "Have no doubt we will send you back like your grandfathers".
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Turkey is heading to key municipal elections which are considered a test for Erdogan's leadership after he considerably strengthened his executive powers following a general election in 2018.
Turkish ambassador Korhan Karakoc said he had a "frank" conversation with Morrison when the envoy was summoned to Parliament House on Wednesday.
He applauded New Zealand Prime Minister Jacinda Ardern for urging Western leaders to "embrace Muslims living in their respective countries".
Judging from the manifesto published by Brenton Harrison Tarrant, the 28-year-old Australian shooter, he was backed by global anti-Islamic forces hostile to Turkey, former Minister of European Union Affairs Egemen Bagis opined in an interview with Sputnik Turkey. Australia also placed under review its travel advisory for its citizens visiting Turkey, which was already set at "exercise a high degree of caution" due to the threat of terrorism.
The comments came after Peters warned Erdogan that showing footage of the shooting to supporters of his Islamist AK party could risk the safety of New Zealanders overseas.
He called on New Zealand to amend its laws to ensure that the attacker, who killed 50 people in two mosques, should be severely punished.
New Zealand authorities moved quickly to try and stop the spread of the shooter's video, warning that anyone sharing the footage faced prosecution, and Facebook removed the images from hundreds of thousands of pages.
"There's a meeting that takes place in the next few days and the New Zealand foreign minister will be there and our ambassador will attend that meeting and there'll be opportunities for further discussion".