Mr Duterte asked Ardern: "You don't have atomic bombs?"
The Philippines and New Zealand signed late Tuesday a memorandum of cooperation aimed at improving the education system in the Southeast Asian nation.
She also has more bilateral meetings before attending the East Asia Summit - a meeting of the 10 Asean countries plus New Zealand, Australia, United States, Japan, South Korea, India, China and Russian Federation.
Earlier on Tuesday, Ardern witnessed the signing of 3 agreements in Makati City - two bilateral agreements and an agreement between the New Zealand government and national flag carrier Philippine Airlines (PAL).
CHED chairwoman Patricia Licuanan and David Strachan, New Zealand ambassador to the Philippines, signed the agreement.
President Duterte said it is a "good development", noting that more Filipinos can have access to the quality of education in New Zealand.
Foreign Minister Winston Peters held a bilateral meeting with his counterpart from China, Wang Yi, a few days ago in Vietnam on the sidelines of Apec, where the issue of Chinese fugitives in New Zealand was discussed.
"I may be able to say they decided right because Auckland treats it citizens superbly", he said.
Ardern added that New Zealand had its first Filipino candidate in their party, Romeo Udanga, to be a member of Parliament during the last election."He did a phenomenal job".
He said he had visited New Zealand twice and was impressed - although he described what seemed to be a run-in with a customs officer. No doubt about it.
Ardern meanwhile said she was pleased to know that there will soon be a direct flight to New Zealand.
There appeared to be some confusion when Ardern mentioned a new deal with Philippines Airlines to fly non-stop between Manila and Auckland, with Duterte instead talking about Iran.
"I'm also looking at the two-way trade that we have, a billion dollars. But I think we have a strong foundation economically", she said.