"The hate speech laws would create a divided and hateful society where cancel culture would spiral out of control," Act leader David Seymour said.
"Faafoi claims that Cabinet will consider hate speech in the next few months but he wouldn't commit to a law being passed before the election," he added.
"It's time to let this misguided policy go. It's okay to admit when you're wrong and move on."
The shooting in a mostly black neighbourhood is believed to have been live-streamed, accompanied with a manifesto, and motivated by anti-black racial hatred.
Former FBI deputy director Andrew McCabe told CNN the Christchurch terrorist might have inspired the 18-year-old supermarket shooter.
Last year the Government unveiled proposals and invited public feedback, including on a new criminal offence with harsher penalties and protections for more minority groups.
The Royal Commission into the 2019 Christchurch mosque attacks found New Zealand's legal system did not adequately deal with hate crime and hate speech.
"The current laws do not appropriately recognise the culpability of hate-motivated offending, nor do they provide a workable mechanism to deal with hate speech," it said.
The Royal Commission said the section of the Human Rights Act criminalising certain types of hate speech was unfit for purpose.
"The section as written unacceptably impinges on the right of freedom of expression."
And the inquiry added: "More generally, it does not provide a credible foundation for prosecution."
It recommended a reframed offence more accurately targeting behaviour warranting criminal prosecution, and encompassing hate speech directed at religious affiliation.