Grey Power president Tom O'Connor said MPs should support Swarbrick's bill at the first reading so it can be explored by a select committee.
"Those with chronic pain should also have access to medical cannabis, if it offers them some relief."
He said health professionals, not politicians, should decide who should be allowed to use cannabis for medical purposes.
Swarbrick said she hoped Grey Power's support would "open the hearts and minds" of MPs who were uncertain about supporting her bill.
She said the Government bill improved the status quo, but was far more restrictive than other international frameworks including the UK, Israel and Canada.
"It would appear as though all jurisdictions that have moved towards changing laws around medicinal cannabis have never constrained access so much as the Government bill would - the criminal defence for those with a terminal illness.
"In New Zealand at the moment, only about 70 people at any given time are able to access medicinal cannabis by jumping through those hoops set up by the Ministry of Health. Even when they can do that, there is massive expense to the tune of about $1200 a month.
"If we were to adopt Israel's approach, approximately 15,000 people in New Zealand would have access to medicinal cannabis. If we adopted Canada's, that would look like 25,000 people having access in New Zealand."
She said a select committee was a good place to deal with the issue of defining chronic pain.
Swarbrick's bill would make it legal for anyone with a qualifying medical condition to grow, possess or use the cannabis plant or cannabis products for therapeutic purposes, provided they have the support of a registered medical practitioner.
A relative or nominated person could also grow cannabis and supply it to the person.
O'Connor said Grey Power supported cannabis-based pharmaceuticals, but not home-grown cannabis for self-medication.
"Self-medication is hazardous at best and, for as long as recreational home grown cannabis is illegal, we cannot support its use for self-medication as it would be too easy to abuse."
The last time a conscience vote was held on medicinal cannabis was in 2008 - Prime Minister Jacinda Ardern supported the bill at the time. She has not yet said whether she would support Swarbrick's bill.
Former Prime Minister Helen Clark, a member of the independent Global Commission on Drug Policy, has shown support for Swarbrick's bill.
A public referendum on legalising cannabis for personal use will also take place by 2020 at the latest, as part of Labour's coalition agreement with the Green Party.
