The Government wants to make live-streaming objectionable material a crime and punishable by up to 14 years in prison or a fine up to $200,000.
And platforms that don't comply with take-down orders could also be stung with a $200,000 fine.
But the bill has been opposed by National, Act, Te Paati Māori and the Greens who called it an "overly invasive regime".
National MP Simon Bridges said it was an extension of the "cancel culture" which led to Magic Talk radio host Sean Plunket losing his job.
"Whatever people think about Sean Plunket, the reality is in the last week or so he's been taken off his radio show by large corporates ... who are scared. They're scared of identity politics and cancel culture.
"It's the easy thing to do is to get rid of him. That's insidious to our culture of freedom of expression."
Bridges said the bill was an internet filter which "fundamentally, arbitrarily" reduced the freedoms of New Zealanders which would drive content underground.
The legislation passed its first reading this afternoon and will now go through a select committee process.
The bill comes in the wake of the March 15 Christchurch mosque attacks which the terrorist live-streamed on Facebook for 15 minutes.
The video was then shared on sites like YouTube and Twitter.
Minister for Internal Affairs Jan Tinetti yesterday introduced an amendment to the Films, Videos, and Publications Classification Act 1993 as part of a wider Government programme to address violent extremism.
Tinetti said bringing live-streaming into the Act meant the Government could act more swiftly if another incident were to ever happen again.
What is considered "objectionable material" is already defined under the Classification Act and usually relates to any publication that deals with subjects like sex, horror, crime, cruelty and violence.
National and Act are opposing the bill on the grounds of defending free speech and the Greens opposed it because at present the legislation would allow the Government to implement a web filter.
Tinetti said she expected the bill to be changed after putting it through a full select committee process - particularly around internet filters.
National's broadcasting and media spokeswoman Melissa Lee said live-streaming was already covered by the Classification Act.
Lee called the bill "censorship legislation".
"What it really means is that this reason why this bill is introduced and the reasoning that the Minister has put forward for the House to consider—literally the argument falls flat on her face," Lee said in the House.
"This is a censorship legislation. It's a farce at its worst. It's actually a censorship legislation at its worst. And she should have asked her officials to provide her with decent advice. Obviously, the former Minister didn't ask the same question either."
She said the legislation was not necessary - it was about the Government wanting to provide an internet filter.
"[It's the] Government deciding what is objectionable and what is not. And once we start down that path, and I'm not so sure where we will actually stop.
"This is an overly invasive regime that encroaches on the rights of individuals."
The Greens' broadcasting and media spokesperson Chloe Swarbrick said the bill was "90 per cent there" but opposed it at its first reading because her party believes it would allow the Government to implement web filtering.
Swarbrick said it could give governments "unbridled power of regulation" and erred "towards far too much authoritarianism" for her liking.
Act leader David Seymour called the piece of legislation "a nonsense that cannot work".
"It will reduce New Zealanders' most basic freedoms to think their thoughts and speak their minds without concern for arbitrary coercion by the State."
Te Paati Māori co-leader Rawiri Waititi also opposed the bill because as it stands it could impact marginalised communities.
The Bill amends the Films, Videos, and Publications Classification Act 1993 so that:
• The Chief Censor will be able to more quickly notify the public of illegal content that could cause high levels of harm;
• The live-streaming of objectionable content will be a criminal offence;
• Government will be able to issue take-down notices, requiring the removal of objectionable content online
• Social media companies will come within the scope of current laws on objectionable content; and
• Legal parameters are established for a potential web filter to block objectionable content in the future, subject to further policy development and consultation.