It also wants to adopt a successful Canadian programme which allows community organisations to take on the responsibility for resettling refugees for a year after their arrival.
The Government is also interested in the Canadian model, and is about to start a pilot programme which will allow NGOs to take on 25 refugees who are able to speak some English and have certain job skills.
Prime Minister Bill English said yesterdaythat the scheme was "very small" and the Government was not committing to "a big shift" in the number of refugees coming to New Zealand.
"The hard work has to go into ensuring that the churches ... can have in place sustained capacity to work with refugees. This isn't just about welcoming people who turn up."
The Greens want a more ambitious community sponsorship programme which can take 1000 refugees, over and above the annual quota. It also wants the programme to be based on need, rather than having language and skills requirements.
The final part of the Greens' refugee policy is to create a new humanitarian visa for climate refugees from the Pacific, which would initially be available to 100 people a year and possibly rise depending on demand.
Residents in Kiribati, Tuvalu and other islands are increasingly threatened by rising sea levels caused by a warming climate. The United Nations does not currently recognise climate change in its refugee-vetting process.
The proposed increase in New Zealand's refugee quota would require a new resettlement centre, in addition to the recently-upgraded centre in Mangere. The Greens would create a new centre outside Auckland, and pay for it by taking 10 per cent of the money raised by the Investor and Investor Plus schemes. Those programmes grant residency to migrants who invest between $3m and $10m.
Where do parties stand on the refugee quota?
NATIONAL: Annual quota of 1000 refugees a year from 2018/19, possibly more if a community sponsorship programme is successful.
LABOUR: Increase quota to 1500 refugees a year over three years.
GREEN: Increase quota to 4000 within six years, with an additional 1000 taken by NGOs.
NZ FIRST: Supports quota of 1000, but only if immigration levels cut and safeguards increased.
MAORI: Increase the quota, consider an emergency intake of 500 people.
ACT: Increase refugee quota in line with GDP growth.
UNITED FUTURE: Increase quota, allow private organisations to play a bigger role in resettlement.