"Political timidity" was holding up reform in this area, he said.
Hague said the policy had been given impetus by the case of Lecretia Seales, a Wellington lawyer who unsuccessfully asked the High Court to give her the legal right to end her life with the help of a doctor.
If implemented, the Green Party's policy would allow terminally ill people aged 18 the right to choose to end their life, if strict thresholds were reached.
It does not go as far as a private member's bill drafted by Act Party leader David Seymour, which gives the option of assisted dying not only to terminally ill people but also to those with "a grievous and irremediable medical condition".
Hague said he had raised the new policy with Labour, which has signed an agreement with the Greens to work together until the election. While it was now formal policy, the Greens were unlikely to campaign on the issue.
Labour has been reluctant to champion reform in the area of assisted dying, saying that it wants to work on issues of greater priority.
Leader Andrew Little told one of his MPs, Iain Lees-Galloway, to shelve a private member's bill which would have legalised voluntary euthanasia, out of concern that it could become a distraction for the party.
Lees-Galloway inherited the bill from former Labour MP Maryan Street, who submitted a petition on voluntary euthanasia to Parliament after failing to get re-elected in 2014.
Parliament's Health Committee is now considering her petition, which called for an investigation of public attitudes to assisted dying and whether the law should change in New Zealand.
