The harm from online misinformation campaigns has been in the spotlight since Russian agents were revealed as using Facebook to manipulate public opinion, including about US politics.
But Ardern said she had no plans to broaden the Christchurch Call, which asks signatories to abide by the principles of free speech and an open, secure internet.
The call also asks countries to ensure societies are resilient against violent extremism, but it does not cover wider issues of misinformation because they are greyer free speech areas.
Ardern did not say whether she thought Singapore's new law was consistent with free speech principles, but Singapore Prime Minister Lee Hsien Loong was adamant that it was.
"I don't see our legislation being in any way restrictive of free speech. There are always rules around what you're allowed to do in terms of freedom of speech, because no free speech is absolute," he said.
Fake news on social media platforms was harmful and required "an immediate response", he said.
"We have to do this and it is a step in the right direction."
The footage of the terrorist attack on March 15 was unrelated to Singapore's new law about fake news, he said.
"His actions in Christchurch, it was not falsehood. It was true, and you have to find ways to prevent that from being circulated."
Singapore has expressed sympathy for the victims of the March 15 attack, but has not signed up to the call nor indicated support for its principles.
Despite the call making it clear that any action should be consistent with free speech principles, the US did not have a representative at the summit in Paris.
The White House said it supported the principles of the call, but had concerns about free speech.
Lee and Singapore President Halimah Yacob hosted Ardern and Associate Trade and Export Growth Minister Damien O'Connor at the presidential residence in Singapore.
The military band played the national anthems of both countries, and Ardern and Lee then inspected the guard of honour before signing the Enhanced Partnership agreement.
The centrepiece was a $57 million funding pool to boost joint research on, among other things, data science and nutrition between the two nations.
Other key features include:
• Enhanced defence cooperation and a new Cyber Security Arrangement
• An improved Working Holiday Scheme
• Visa-free access for New Zealanders to Singapore for up to 90 days
• A suite of Arts and Culture agreements
At a press conference afterwards, Ardern and Lee both expressed concerns about the impacts of ongoing US-China trade fictions.
Lee said both New Zealand and Singapore were small, trade-reliant nations and it was important to continue demonstrating the benefits of free and open trade relationships.
Singapore is New Zealand's seventh largest trading partner, with trade between the two nations worth $5.2 billion in 2018.
Singapore is also the eighth largest source of tourists, with 61,000 visitors a year, and the fifth largest foreign investor with $4.32 billion.
