National has lodged a notice of a motion of no confidence in Parliament's Speaker Trevior Mallard over his handling of the Parliament protesters.
It comes on day nine of the protesters' occupation on Parliament grounds.
Chris Bishop today described Mallard's behaviour as "unedifying, embarrassing and childish" after the sprinklers were turned on and protesters were subjected to Barry Manilow music.
"Many New Zealanders are appalled and so are we," Bishop said.
"You can disagree with people without disrespecting them, and Mr Mallard's petulant behaviour has only inflamed an already tense situation."
National has repeatedly sought motions of no-confidence in Mallard with no success.
It comes over a week since Covid response protesters first brought parts of Wellington city to a standstill, with police and council have now signalled they will be taking a firmer line.
Meanwhile Act leader David Seymour says he's met with some of the anti-mandate protesters' leadership, and said it's time for a 'mature conversation' about de-escalation.
The Act leader said he'd met with several dozen people linked to the protest, and changed his mind after a local bar owner told him the protest situation was changing and the worst elements had left.
"The people involved in the protest, while some of them have engaged in reprehensible behaviour, and the protest altogether continues to make unacceptable interruptions to Wellingtonians going about their life, are nonetheless people who are human, who are part of New Zealand."
"And eventually we need a way to glue this country back together when this is all over."
Seymour said there was no chance of him or probably any MP meeting protesters as long as Victoria University was occupied and nearby streets were blockaded.
It comes after Cabinet Minister Megan Woods told Newstalk ZB's Mike Hosking earlier that it is not true that any government ministers will meet with protesters or their representatives today.
The principal of a Wellington school says they are now advising all staff and students to take alternative routes to school after "confronting" experiences with anti-mandate protesters at the start of the protests.
Queen Margaret College principal Jayne-Ann Young said uniformed children on the way to school, some under 10, were verbally abused for wearing masks.
"People were coming up to them, very close, unmasked, and they were being told masks were unnecessary, Covid is not a problem and it's all just rubbish."
About a kilometre away from the protests on the Parliament lawn, classes and activities at the Wellington girls' school are otherwise unaffected.
Wellington City Council said they yesterday issued about 335 tickets to illegally parked vehicles in the area of the protest, bringing the total to more than 500 fines.
In an update this morning they said a dedicated council team has been established to address the wide-ranging operational issues with the protest.
The statement said the council team was following "every possible route and option", but for security reasons they were unable to provide detailed information at this time.
"Where we can, we will keep Wellingtonians informed of developments, but we ask for your patience and tolerance while we work to resolve this difficult situation."
Police Commissioner Andrew Coster said this morning towing trucks will begin removing vehicles today.
Speaking with Mike Hosking, he said they've also appealed for more assistance including from the New Zealand Defence Force for their towing capabilities.
On whether the police were doing enough he said it was important they took a measured approach.
"If we went in there early on guns blazing that we would have had a much messier and problematic situation on our hands.
"What we need here is a resolution that means normal people can go about their normal lives safely and that calls for a measured approach on police's behalf."
Appearing on AM earlier, Coster said towies would be required to move the vehicles, but they would be supported by police officers.
"We are not seeking an escalation here, we just need to clear the roads," he said.
"We are engaging with protesters about the manner of the protest. But there has to be a line here - this can't go on indefinitely.
As at 11am, towing of protesters vehicles had not yet begun, according to reporters on the ground.
A video posted on social media yesterday showed a police car being towed from outside Wellington's central railway station, which is very close to the protest site. A police spokesperson confirmed the vehicle needed to be towed as it had a puncture.
With the protracted standoff in its eighth day yesterday, protesters claimed they want to minimise disruption and plan to work with police to identify rogue elements in their midst.
Protesters have been told to move their cars out of the bus lane so children can catch school buses, and an NZME reporter on the scene said it appeared some had followed this instruction.
The group said it had received no response to a request to meet Cabinet ministers, but police had acknowledged their right to protest on Parliament grounds.
Earlier police attempts to persuade occupiers and demonstrators to move vehicles to Sky Stadium were unsuccessful, with some protesters believing the offer was a trap.
Yesterday afternoon, Coster said many people at the protest had a lot of mistrust but he encouraged vehicle owners to act in good faith.
The ongoing disruption had become "untenable" and police were now preparing to tow vehicles to free up roads.
Coster said police would tolerate lawful protest and it would probably take a few days to clear all the vehicles.
"We have made a request to the New Zealand Defence Force for assistance with towing and we are awaiting the outcome of that request," he added.
It's understood the Defence Force was considering its options yesterday afternoon and deciding how to respond to Coster's request.
Under the Defence Act, any involvement by the Defence Force in helping clear the protest could require either the Prime Minister or Defence Minister to authorise it.
In a statement, the Defence Force said: "There are a number of factors to be considered not least the suitability of military recovery vehicles for this task and the availability of trained personnel, which we have discussed with NZ Police. Discussions are ongoing.
Police also appealed to tow truck operators to help, earlier saying safety concerns had prevented them from taking up the task.
However RNZ reports the real reason many tow truck companies did not want to get involved was because they sympathised with the protesters.
"There's all different reasons being put forward, but the reason that the majority of my colleagues don't want to put their tow trucks out there is because they are sympathetic to what's going on in Parliament," said Greg Cox, who owns Wellington's Cox Heavy Salvage.
Not wanting to sour their relationship with police, Cox said some operators had made up excuses for not lending a hand in the towing operation.
Speaking to RNZ, Wellington mayor Andy Foster said they had been engaged with the tow truck companies contracted by the council and the feedback was they were under significant pressure and had threats made to them.
"They are frightened."
To his knowledge none of them had declined on the grounds that they supported the protest.
Foster wasn't "particularly keen" to walk through the protest site as it could feel potentially intimidating, especially if you were recognisable, but he had spoken to some people on the edges.
"The reality is there's a mixture of people - I think most people are being peaceful and I think most people you can go and have a conversation and feel for what they are thinking."
The protesters would all do themselves a big favour if they stopped anybody behaving badly and removed any offensive signs such as photos of nooses hanging, he said.
"They would look more credible in the eyes of the wider public. Those sort of things always will let any movement down."
Luxon: 'Some really good people in there'
Meanwhile National Party leader Christopher Luxon says he still feels safe inside the Parliament building, but is feeling for the people of Wellington who have been affected.
Luxon has had to move out of his usual apartment due to the interruption caused by protesters.
Asked if he felt safe, he told TVNZ's Breakfast show: "I feel really safe."
Asked how he would have responded to the protesters had he been in Government, he acknowledged how frustrated many businesses and ordinary Kiwis were now.
Luxon told Breakfast the protest is interesting and that there is a real wide range of groups and people outside Parliament's doorsteps.
"There is some really good people in there, but there's a real range of people and views in there as well."
A statement attributed to seven groups, including Freedom Alliance, Convoy 2022 NZ and The Freedom and Rights Coalition, said protesters were a diverse group that believed mandates "must end".
The group tried to distance itself from claims occupiers have harassed passers-by, spat at a bus driver, and bullied children for wearing masks.
"We are a peaceful movement and do not condone or tolerate aggression or intimidation. We have a dedicated internal security team to maintain a peaceful operation.
"We speak for the vast majority of the protesters present, but not all. Accusations have been made about threatening behaviour and we encourage the police to work with us on that to identify those involved."
The groups said they were mindful of public safety and wanted to minimise disruption to the people of Wellington.
"We strongly urge the government to engage – they want a solution, we want a solution."
Protesters continued to sing, dance, chant and give speeches yesterday.
Kita, 21, said she'd been staying on Bunny St near Parliament for the past week.
"It's not right, they shouldn't be doing that, because we are here for something important," she said.
Some protesters were seen removing number plates and registration to avoid being ticketed. Others attached fake plates instead.
The protesters have aired a range of views and grievances.
"There's just so much bureaucracy that's making it hard to get ahead in New Zealand," one speaker said.
Although vaccine mandates and broader restrictions related to Covid-19 have dominated protester discussions, that speaker also spoke of the country's housing crisis.
A boy performed hula hoops in front of a barrier separating police from protesters.
Later, protesters were being treated to a new form of entertainment - Parliament TV.
The live account of events inside the building was streamed through loudspeakers set up by Speaker of the House Trevor Mallard.
But demonstrators had several loudspeakers of their own, trying to drown out the sound of Parliament TV.
The protest groups said it was unable to respond to specific media questions but was working to appoint a spokesperson and hoped to provide answers "in the coming days".
"We therefore challenge Labour to run a national poll and share the results, asking New Zealanders: 'Do you support the mandates?'"
Meanwhile, Prime Minister Jacinda Ardern said she was receiving regular updates from police on the protest.
Asked how long she would tolerate the protest lasting, Ardern replied: "That's actually not the question for us. Ultimately, of course we have protests in this place all time, and we accept that as politicians."
The PM added: "But what we've seen out here is something quite different."