"It's one of the reasons I feel quite strongly about this policy."
The 2003 movie depicts a secret relationship between a closeted Mormon and an openly gay friend.
Ms Ardern was raised a Mormon but left the church in her 20s in solidarity with gay friends.
Conversion therapy is the medically illegitimate practice of attempting to change someone's sexual orientation or gender.
It has been banned in Queensland and the ACT, with Victoria also seeking to change its laws to outlaw the practice.
In New Zealand, Ms Ardern has been criticised for not implementing a ban in her first term, given both her Labour party and coalition partner the Greens support it.
A parliamentary report last year recommended against banning the practice, suggesting it could be a breach on religious freedom, as the therapy is most often pushed by conservative religious groups.
Kiwis are overwhelmingly for a ban; a TVNZ poll found 72 per cent in favour of outlawing the practice.
"We need numbers in the house to pass legislation," Ms Ardern said.
"So what I'm committing to is ... our numbers to delivering this and I hope there will other parties in parliament who will support it."
Opposition leader Judith Collins has also signalled her opposition to conversion therapy.
"I'm a parent and I have said to my son, and I hope other parents would also say this, 'Just be who you are'," she said.
"That's the best thing any parent can do. Not trying to convert your child to anything else."
If given a second term, Labour will also seek laws to make it easier for transgender Kiwis to change their gender on their birth certificate.
Ms Ardern's government failed to do so during their first term.