The law that allows for assisted suicide will go into effect in one year's time.
Assisted suicide and euthanasia are only legal in a handful of countries and jurisdictions around the world, including Switzerland, the Netherlands, and Canada.
Ms Ardern said on Friday after the results were released that she had voted in favour of both referendums.
National's Nick Smith said New Zealand would be "healthier, safer and more successful for rejecting the legalisation of recreational cannabis".
It's a yes to euthanasia and a no to cannabis, at this stage.
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The results do not include an estimated 480,000 special votes including postal and overseas ballots, so the full outcome will not be confirmed until next Friday.
The results could impact the final referendum results.
New Zealanders were asked whether they agreed with the End of Life Choice Bill, which allows assisted dying for people with terminal illnesses subject to a range of conditions and safeguards. Some European countries, including The Netherlands and Belgium, as well as Canada and Colombia allow some form of euthanasia, as do some U.S. states.
The lawmaker behind the reform, libertarian David Seymour, said it was a "resounding victory" that would make New Zealand more compassionate and humane.
It is also allowed in a number of USA states and the Australian state of Victoria, while some counties allow "assisted suicide", where the patient self-administers fatal medication, rather than a medic or third party.
If passed, the cannabis law would allow adults who were at least 20 years old to buy up to 14 grams (0.5 ounces) per day and grow two plants. Ardern has previously supported legalizing cannabis in the country.