ACT leader David Seymour's euthanasia bill has been pulled from the members' ballot and will go before Parliament.
Mr Seymour's bill would allow for assisted dying in the cases of people who are terminally ill but still mentally sound.
His End of Life Choice Bill will be debated on the next members' day, likely either immediately before or after the election in September, and political leaders said it would most likely be a conscience vote for their parties.
Mr Seymour said he was "confident" of getting enough support to get the legislation over the first hurdle.
"This bill will pass a first reading, however there is going to be a lot of work to do and it is going to depend on Members of Parliament looking to their electorates and the people who elect them and pay their salaries to understand what people want," he said.
Mr Seymour said his last count of MPs had 40 strongly in favour, 27 opposed and about 50 undecided.
Mr Seymour said the "campaign starts now".
"We are long overdue for a compassionate response to the anguish faced by the small but significant minority of grievously and irremediably ill, or terminally ill, people," said Mr Seymour.
He said the current law left them no choice but to endure "intolerable suffering and loss of dignity" in the final days of their lives.
How will MPs vote?
Prime Minister Bill English will vote against the bill, as will the senior minister Gerry Brownlee.
Deputy Prime Minister Paula Bennett said she was undecided. Ministers Steven Joyce, Simon Bridges and Nick Smith all joined her in their indecision.
"I'm pretty conservative on these issues," Mr Bridges said. "I'm very likely to vote against it ultimately... I might vote to see it go to a select committee so that the issues... are fleshed out."
Labour MP Grant Robertson said he would support the bill at its first reading.
"It's a really important conversation for New Zealand to have."
The Green Party intends to vote as a bloc, but was yet to discuss its stance on Mr Seymour's bill.
Its policy is to support medically-assisted dying for adults with a terminal illness, however this legislation also includes people with a "grievous and irremediable medical condition".
New Zealand First MPs said they would discuss the bill as a caucus before deciding how to push forward.
The party's policy was for New Zealanders to have a national discussion over at least two years followed by a binding referendum.
The Māori Party's Marama Fox said both she and her co-leader, Te Ururoa Flavell, intended to vote against the bill.
"I've sat holding the hands of dying people over and over again from my own family. I can't even remember going to a funeral where it was of natural causes in the last 28 years... I've never once had any one of those people say they wanted to go early. Not once."
Time to turn public support into action - Seymour
The Health Select Committee is currently considering public attitudes to voluntary euthanasia after receiving submissions from thousands of people.
The Death with Dignity Bill was put to Parliament in 1995 and 2003 but failed to pass; in 2012, the End of Life Choice Bill was also unsuccessful.
Mr Seymour said there was a lot of public support for allowing assisted dying for those with terminal illness or who were grievously and irremediably ill.
"It's time to translate this support into action."
Earlier this year, a New Zealand Medical Journal study showed there was growing support for euthanasia in New Zealand, especially from younger people.
It asked nearly 16,000 people if those with painful incurable diseases should be allowed by law to end their lives.
The survey found 66 percent were in favour, 22 percent were neutral or unsure, and 12 percent were opposed.
Awareness of euthanasia had grown in the last few years after cases such as that of Lecretia Seales, who fought to change the law while terminally ill.