They said the government had an important role to play as an employer of "setting an example of what fair employment practices and good conditions look like".
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Labour estimated thousands of workers were likely to benefit from the policy - 400 security guards were paid the living wage when it was rolled out to contracted guards at the Ministry of Social Development.
The policy would cost the government $18 million more a year.
"Covid-19 has shone a light on the many workers who do important work in our community but who are not well paid for it.
"We can do a lot better at lifting wages and easing financial stress for hard-working New Zealanders," said Little.
He said the policy built on the Government's move in 2018 to pay all core public service staff at least the living wage.
Twyford called contracted workers the "backbone" of the public service and said paying them a living wage was "a win for everyone".
"These are the workers that clean the office late at night, start work early to cater for conferences and stand in the cold making sure our offices are safe for everyone. The work contracted employees do help us all to do our jobs.
"Paying contracted workers a living wage will be a great boost to their household incomes and improve life for them and their families.
"This money will be spent back in the community, meaning it will benefit the wider economy at the same time."
As current contracts end, public service agencies would be required to guarantee the payment of a living wage as part of new contracts. Labour expected the policy to be fully in place within the next parliamentary term.
The living wage is calculated independently each year by the New Zealand Family Centre Social Policy Unit and reflects the basic expenses of workers and their families like food, transport, housing and childcare.
Core government agencies include:
Crown Law Office, Department of Conservation, Department of Corrections, Department of Internal Affairs, Department of the Prime Minister and Cabinet, Education Review Office, Government Communications Security Bureau, Inland Revenue, Department of Land Information, New Zealand Ministry for Culture and Heritage, Ministry for Pacific Peoples, Ministry for Primary Industries, Ministry for Women, Ministry for the Environment, Ministry of Business, Innovation, and Employment, New Zealand Police, Ministry of Defence, Ministry of Education, Ministry of Foreign Affairs and Trade, Ministry of Health, Ministry of Housing and Urban Development, Ministry of Justice, Ministry of Māori Development, Ministry of Social Development, Ministry of Transport, New Zealand Customs Service, New Zealand Security Intelligence Service, Oranga Tamariki—Ministry for Children, Serious Fraud Office, Public Service Commission, Statistics New Zealand,Te Kāhui Whakamana Rua Tekau mā Iwa—Pike River Recovery Agency, The Treasury.