He said "the enemies of Muslims have shown that they continue to hate us".
"They are testing us from 16,500km away, from New Zealand, with the messages they are giving from there. This is not an individual attack, it is organised."
At the weekend Erdogan used extracts of video footage of the attack in one of his election campaign rallies to condemn Islamophobia in Western countries.
Peters said he was heading to Turkey to put the record straight.
"They asked me to come and I'm going to go.
"I certainly intend to put New Zealand's record as being an innocent party to an act of a foreigner in our country."
He had made that clear on Sunday when he met Turkey's Vice President Fuat Oktay, and Foreign Minister Mevlut Cavusoglu in Christchurch, and they had left at 4am this morning.
"They'll have a chance to put the record straight when they get home."
On Monday Peters said that playing the video of the massacre misrepresented New Zealand, it was unfair and put the safety of New Zealanders abroad at risk.
Peters is leaving tonight for a pre-scheduled visit to Indonesia. After that he would be heading to Turkey, having been invited this week to attend the Organisation of Islamic Co-operation in Istanbul.
"This is not the act of a New Zealander," Peters said. He had been contacted by many foreign ministers all around the world.
Australian Brenton Tarrant, who has recently been living in Dunedin, has been charged with murder after a rampage through two Christchurch mosques on Friday killed 50 Muslims.
He visited Turkey in the past few years and in literature he published minutes before the attacks, he directs hateful comments at Turkey.
Erdogan said he had spoken to New Zealand's Governor General Dame Patsy Reddy to emphasise New Zealand should respond seriously.
The fiery address will heighten New Zealand authorities' concerns about the reaction internationally to the mosque attacks, particularly before Anzac day is commemorated on April 25.
It is something of a pilgrimage for New Zealanders and Australians to visit Gallipoli on Anzac Day.
While the Ministry of Foreign Affairs has issued general advice to New Zealanders to be cautious about any adverse reaction overseas, it has not yet issued advice specific to any one country.
It is understood some New Zealand missions overseas have reported concerns about hostility toward New Zealanders in the days after the attack last Friday. New Zealand is expected to soon boost its diplomatic response, especially in countries with significant Muslim populations, to try to limit any response.