"In short we made it very clear that we oppose terrorism in whatever shape and form it might be and that we are for a free and open society.
"We had a long dialogue on the need for any other country, or Turkey for that matter, to ensure that our country, New Zealand, was not misrepresented.
"We did not start or bring about this disaster and they clearly understood that," Peters said.
Australian citizen and white supremacist Brenton Tarrant has been charged with murder following the killing of 50 people praying in two mosques during a rampage which he live-streamed on social media.
Turkish elections are due to be held on March 31 and Erdoğan has used some footage of the attack in a televised election campaign rally to condemn Islamophobia.
Tarrant visited Turkey twice and in recent years and made several hate-fuelled references to the country in his so-called manifesto published minutes before the massacre.
Ardern said that Peters was right in saying that the primary suspect in the terrorist attack was not a New Zealand citizen.
"However that is not to say that there are not those who live in New Zealand who hold values and ideas and use language that is completely counter to what the vast majority of New Zealanders believe and so I don't think we can ignore that. In fact, we cannot ignore that if we are to continue to ensure the safety of our Muslim communities and others, the 200 ethnicities that live in New Zealand, we have to be live to the fact that there are those who do not share our values of openness, of diversity, of compassion and that is something we are going to have to confront as a nation."
Meanwhile, New Zealand's Ministry of Foreign Affairs has just posted a new advisory on safetravel.govt.nz warning New Zealanders travelling to be careful in the wake of the attacks.
"The terrorist attacks in Christchurch on 15 March, which were motivated by extreme right-wing ideology, have attracted global attention and strong international condemnation. International reactions to those events are difficult to predict and may change at short notice."
It says New Zealanders should "use common sense, exercise caution and be vigilant."
"They should look out for and report suspicious behaviour, as they would in New Zealand. New Zealanders should continue to monitor the media and other sources for information about possible new safety or security threats, and follow the advice of local authorities. New Zealanders should also continue to avoid demonstrations and protests, as they can turn violent."