Greens co-leader Marama Davidson can't reveal when Dr Kerekere 'crybaby' investigation will end

The Green Party co-leaders are refusing to provide any new information on the investigation into MP Dr Elizabeth Kerekere as its rolls into another week.

They're not committing to any timeline and say getting an external party in to carry out an investigation remained an option.

Dr Kerekere was last month reportedly caught calling fellow MP Chlöe Swarbrick a "crybaby" and further allegations of bullying have since emerged in the media from anonymous sources.

The MP wasn't at Parliament on Tuesday - she's attending a tangi this week - but her party co-leaders fronted media on the way into the House. 

"We are just getting on with the mahi and the work," said Marama Davidson. "It's an internal process so we wanna keep it fair and we're unable to make any further comment."

She said the party couldn't commit to a timeline and bringing in an independent party to carry out the investigation was "an option".

"We are unable to provide any further details on how that process is running at the moment."

The process is being conducted by musterer (whip) Jan Logie and chief of staff Robin Campbell. 

The investigation is occurring as the Green Party goes through its list process. 

Some party members last week unsuccessfully tried to delay voting on the list until after the investigation is completed so that members would have more information when making their decisions about MPs' positions. 

Davidson was asked whether people making anonymous comments criticising Dr Kerekere's conduct was dirty politics with the intent of trying to get rid of her.

She said the co-leaders wanted to keep the process fair, but "what happens outside in other people's privacy is up to them". 

"There's an internal process and we really just cannot comment any further because we're trying to keep that process strong and robust."

It emerged in early April that Dr Kerekere accidentally sent a text message to a group chat with other MPs calling Swarbrick a "crybaby". 

She later acknowledged she "wrote an inappropriate message" and sent it to the wrong group chat. But she denied calling Swarbrick a crybaby when contacted by RNZ.

Davidson at the time said the message was disappointing as the party is "about celebrating each other and working together hard to get stuff done".

"We have always been really clear about supporting each other individually and collectively as a caucus and this appears to have not met those standards from our MPs. So we are disappointed. We will be fully investigating. We are taking this really seriously."