On the last conscience vote to be held in Parliament, for the legalisation of same-sex marriage, the Prime Minister also confirmed early in the process that he would support the legislation, which later passed easily.
Mr Seymour began work on his End of Life Choice Bill after another bill, originally sponsored by former Labour MP Maryan Street, was removed from the ballot.
His bill had stricter safeguards than Ms Street's bill, including a requirement that a person was likely to die within six months, instead of 12 months. They would also need to have approval from two doctors.
If the bill was pulled from the ballot, MPs would cast a personal vote instead of voting along party lines.
Green Party co-leader James Shaw said he personally supported the bill, but his party did not have a position on the issue.
Labour leader Andrew Little has previously said he would support a law change.
Ms Street has not given up campaigning for assisted suicide and was at Parliament yesterday to speak to a select committee about euthanasia.
She told the Health Committee that Parliament was underestimating the public's support for legalising the "right to die".
The committee's inquiry came after the death of Wellington lawyer Lecretia Seales, who in her final weeks unsuccessfully sought a High Court ruling which would have allowed her doctor to help her die without criminal prosecution.
Ms Seales' husband Matt Vickers was also at Parliament yesterday for the beginning of the inquiry.
Speaking about the bill, Mr Vickers and his supporters said in a statement that Ms Seales would have supported any serious effort to improve current laws.
"David Seymour's bill is appropriately narrow, has substantial merit and we wish it well."
