When Derbyshire pointed out she was a feminist, Ardern replied: "Absolutely I'm a feminist. But I want to put him through the pain and torture of having to agonise about that question himself.
"No, that's letting him off the hook. Absolutely not," she said, laughing.
A ring, thought to be diamond, was spotted by reporters on the PM's hand at a ceremony at Pike River on the West Coast today,
Ardern, 38, has previously quashed speculation she and Gayford were engaged.
In December 2017, two months after she became New Zealand's 40th Prime Minister, Ardern addressed speculation about a ring seen on a finger of her left hand.
"I thought I would upfront address the speculation in the gallery this afternoon over my Facebook Live and the issue of where my ring was placed during that Facebook live," Ardern told media at a post-cabinet press conference.
"I'm happy to confirm that I have eczema on my left hand, which causes me to rotate where I wear my beautiful onyx ring. So no I am not engaged", she said at the time.
"I do however suffer from a small skin condition, which is not very romantic. Glad to have cleared that up."
Congratulations to NZ Prime Minister Jacinda Ardern and Clarke Gayford engaged, via @nzheraldhttps://t.co/orzf4Z8MzO. So happy for you both and little Neve ๐