Prime Minister John Key has previously said that while he has voted in favour of voluntary euthanasia in the past, he believed a member's bill was the best way to deal with the issue.
A parliamentary inquiry into voluntary euthanasia began in June. It was prompted by a petition which followed the death of Wellington lawyer Lecretia Seales, who unsuccessfully sought a High Court ruling that would have allowed her doctor to help her die without criminal prosecution.
Mr Seymour did not want to wait for the outcome of the inquiry.
His bill was based on an earlier piece of legislation drafted by former Labour MP Maryan Street. Ms Street removed her bill from the ballot in late 2013 because colleagues were concerned it would be pulled out in election year and become a political football.
"Kiwis want parliament to act"
Mr Seymour said he expects the bill to have support from the majority of New Zealanders.
He told Newstalk ZB that if the Bill was pulled from the ballot today, he thought it would be supported by the majority of New Zealanders and politicians alike.
"My gut feeling is that it would [have enough votes to pass]...but that remains to be seen.
"I think that parliament has to confront this issue. It's easy to find excuses but the fact of the matter is that the overwhelming majority of New Zealanders want parliament to act."
The Bill was very "clear and modest" and had clearly defined safeguards and protections built in, he said.
But he did admit there would be "strong opposition" in each political party.
Family First has hit out at the Act leader's Bill, saying it's premature, and "pre-empts an important national conversation that's just getting under way".
"David Seymour should wait for the inquiry that he supported to be completed. Rather than a flawed euthanasia bill ... it makes absolute sense to debate euthanasia within the wider context of the premature ending of one's life," the group's national director Bob McCoskrie said.
"The country needs to have a robust honest debate about euthanasia without the emotion of a law change in the mix, and examine whether so-called safeguards deserve that label, whether coercion is subtle but real, and whether patients will ask themselves why they are not availing themselves of assisted suicide."
Additional reporting: NZME