
On Tuesday National MP Catherine Wedd, with the backing of leader Prime Minister Christopher Luxon, put forward a members' bill which would follow Australia's lead on cracking down on the social media giants.
The proposed law would require age verification measures on social media platforms.
Luxon said he wanted to explore picking it up as a "broader government bill", which would mean it could become law more quickly.
On Tuesday speaking at Parliament, Act leader David Seymour said National's proposal was "simple, neat and wrong".
"Just slapping on a ban - hastily drafted - won't solve the real problem. The real problem has to involve parents. This solution proposed by National doesn't."
On Wednesday morning a letter penned by Act MP Dr Parmjeet Parmar to the chair of Parliament's education and workforce committee was released.
It proposed an inquiry which would look at the harms of social media for young people.

In the letter Parmar said there had been a troubling rise in mental distress among young people.
She said there was a growing consensus that mobile phones and social media were detrimental to children's development.
"Educators and principals across the country have observed that students arriving at school are more needy and distracted than they were 15 years ago."
Parmar said the National Party's members bill was not workable and that it was "imperative" Parliament not hastily adopt an Australian-style social media ban without an understanding of its impacts.
"Instead, I propose that the Education and Workforce Committee undertake a detailed inquiry."
In a press release she said the proposal to simply ban social media for those under 16 was unlikely to solve the problem.
"Technologically, it's a mine field. Morally, it is a government solution that does not involve parents. Its unintended consequences could do more harm than good."
Parmar said just implementation of a ban could fail technically due to people getting around it, it could drive people to darker parts of the internet and make people less likely to discuss harm they face on the internet.
She also said a ban would erode personal responsibility.