Erdogan's comments at a series of election campaign rallies - including calling on New Zealand to restore the death penalty and repeatedly showing video footage of the shootings that the alleged gunman had broadcast on Facebook - triggered a diplomatic dispute between the nations.
"We are returning home to New Zealand with grateful reassurance that our people who come here to commemorate ANZAC will be as welcome as they always were", he told reporters. He screened photographs of New Zealanders mourning the victims.
Peters said "no punishment can match the depravity of his crime but the families of the fallen will have justice".
"Just as humanity fought against anti-Semitism after the Holocaust disaster, it should fight against rising Islamophobia in the same determined fashion", Erdogan told an emergency meeting of ministers from the Organisation of Islamic Cooperation in Istanbul.
In an address to leaders of Muslim countries attending the OIC meeting, including Iranian foreign minister Mohammad Javad Zarif and Saudi Arabia's ambassador to Turkey, Peters defended New Zealand's response to the shooting and said the perpetrator would spend his life in prison.
Erdoğan praises New Zealand PM after row over mosque attacks
The embassy released a statement on Sunday afternoon saying the country wanted to "categorically rule out" the existence of a security threat against New Zealanders.
"Our police have started the largest investigation in our history", said Peters, who had earlier condemned Erdogan's airing of the footage as risking endangering New Zealanders overseas. It also demanded that March 15 - the day of the Christchurch attack - be marked as the International Day of Solidarity Against Islamophobia.
Mr Erdogan said part of gun suspect Brenton Tarrant's manifesto was to keep Turks from Europe.
"Politicians who pave themselves the road to power by alienating Muslims and creating enemies out of refugees, must pull themselves together", he said.
He also called for neo-Nazi groups to be considered terrorists.
"It's not on, it's not appropriate and it's not the basis of the relationship that we've had really since the end of the first world war with the government of Turkey", he said.More news: Sizzling Tea Practically Doubles Threat Of Esophageal Most cancers: Research
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