The first refugee to be elected to New Zealand's parliament resigned on Tuesday over alleged shoplifting, which she said was related to personal stress and trauma.

Golriz Ghahraman, an MP for the centre-left Green Party and its justice spokesperson, is being investigated by police after three allegations of retail theft.

The lawmaker, a former human rights lawyer, said her actions were "not a behaviour I can explain".

But Ghahraman conceded she had fallen short of the standards expected of politicians and needed time to address her mental health.

Work-related stress led her to "act in ways that are completely out of character. I am not trying to excuse my actions, but I do want to explain them", she said in a statement.

"The mental health professional I see says my recent behaviour is consistent with recent events giving rise to extreme stress response, and relating to previously unrecognised trauma.

"I have let down a lot of people and I am very sorry. It's not a behaviour I can explain because it's not rational in any way, and after medical evaluation, I understand I'm not well."

Iran-born Ghahraman, 42, moved to New Zealand as a child with her family who were granted political asylum as refugees.

After studying law, she became a United Nations human rights lawyer, working on international criminal tribunals before entering parliament in 2017.

The theft accusations surround two alleged incidents at an Auckland luxury clothing store and another at a Wellington clothes retailer -- all in late 2023.

Last week, the Greens announced that Ghahraman had stood down from her portfolio responsibilities while a police investigation was ongoing.

The party's co-leaders, Marama Davidson and James Shaw, in a separate statement, said Ghahraman had been a leading voice for human rights but "it is clear to us that Ms Ghahraman is in a state of extreme distress".

"She has taken responsibility and apologised. We support the decision she has made to resign." (AFP)