"I would tell her: 'girlfriend, you are so on', because the United States of America is going to be the best place in the world for a child to grow up."
The response prompted mocking headlines, including in the Washington Post and the Daily Mail and a storm of replies on social media.
Satirical politics show The Daily Show was quick to jump in:
In a performance that included several other unusual highlights, Williamson also went on to say she would also "harness love for political purposes" to win the presidency.
Later, Williamson doubled down on her challenge to Ardern in a video posted on her Twitter account, saying: "I will call Jacinda Ardern, if that's how you pronounce her name, who is the Prime Minister of New Zealand, because she has said that she wants New Zealand to be the country that is the best in the world for a child to grow up.
"And I want to call her and say 'girlfriend, it is on', because I want the United States to be that too."
When asked by reporters about the New Zealand comment, Williamson reiterated that she wants the US to be the best place in the world to raise a child but it's "fine for New Zealand to be as good".
Ardern has long held that one of her goals in Government is to make New Zealand the best place in the world for children.
The Prime Minister has had a high profile since the Christchurch shootings in March. The image of Ardern embracing a woman at the Kilbirnie mosque in Wellington featured on the Burj Khalifa, an 829m skyscraper in Dubai, United Arab Emirates, and a giant mural of the same photo was painted on a street silo in Melbourne.