A New Zealand MP has resigned following multiple allegations of shoplifting, which police are investigating.

Golriz Ghahraman, of the Green Party, is alleged to have stolen three times from two clothing stores - one in Auckland and the other in Wellington.

The former UN human rights lawyer made history in 2017 as the first refugee in the country's government. She once held her party's justice portfolio.

Work-related stress made her behave completely out of character, she said.

"I have let down a lot of people and I am very sorry," she added.

Ms Ghahraman fled Iran as a child with her family, who were all granted political asylum in New Zealand.

Her resignation on Tuesday comes after CCTV footage emerged showing her allegedly taking a designer handbag from an Auckland boutique.

The 42-year-old, who has not been charged with any crime, said in a statement her actions had "fallen short" of the high standards of behaviour the public expected from elected representatives.

"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," she said, adding that she did not want to make excuses for herself.

"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."

Responding to her resignation, Green Party co-leader James Shaw said that Ms Ghahraman had been subject to "pretty much continuous threats of sexual violence, physical violence, death threats since the day she was elected to Parliament".

"That has added a higher level of stress than is experienced by most members of parliament," he said.

"There have been police investigations into those threats almost the entire time that she has been a member of parliament, and so obviously if you're living with that level of threat in what is already quite a stressful situation then there are going to be consequences for that".

Ms Ghahraman has spoken out in the past about the abuse she has received both online and in person based on her Iranian heritage, her gender and the public stances she has taken on various issues.

"Eventually some of the online threats I faced got to the point where I had to carry a security alarm and have security escorts back and forth from Parliament," she told national broadcaster TVNZ in 2021.

In 2017, Ms Ghahraman was given an escort following threats by white supremacists.

More recently, she has been criticised for taking part in pro-Palestinian protests and for being critical of Israel's military actions in its war against Hamas in Gaza in her role as the Green Party's foreign affairs and human rights spokesperson.

Fellow Green Party co-leader Marama Davidson said it was right that Ms Ghahraman had resigned but that it was clear she was in distress and would continue to receive their support.

"We have seen the conversation over the past years, especially over the particular treatment of women with public profiles, and in addition, the particular treatment of women of colour with public profiles," said Ms Davidson.