A combined statement from groups of protesters at Parliament grounds says they are "disappointed" that a letter sent to the government on Monday asking for talks has been "ignored".
People are outside Parliament for a ninth day in a row, protesting against a range of Covid-19 measures imposed by the government, including vaccine mandates, by occupying the area with vehicles, pitched tents and marquees.
In a statement, the groups said there had been "significant progress" moving vehicles from CBD, and any "aggressive action" by police to move cars would be inappropriate.
"It is clear that the police now accept that the protest on Parliament grounds is lawful.
"This is a sensitive situation but we are confident of a successful resolution.
"We are in regular dialogue with the police, local businesses and Wellingtonians."
They said they had secured a "highly experienced mediator" to facilitate dialogue.
Yesterday, protesters were given an ultimatum by police to move their cars or they would be towed and that warning was reiterated this morning, but the day has passed with no action.
Police this afternoon said more than 400 vehicles remained blocking streets and only about a dozen left the blockade today.
"As the commissioner alluded to yesterday, this remains an incredibly challenging and complex situation to manage," said Assistant Police Commissioner Richard Chambers, who is also the head of the police operation overseeing the protest activity at Parliament grounds.
"Police are taking care not to escalate matters unnecessarily."
Crowds started flooding Parliament grounds on 8 February, and have only grown in number since with many pitching tents and marquees.
The letter on Monday was sent on behalf Convoy 2022 NZ, Freedom Alliance, New Zealand Doctors Speaking Out with Science, Outdoors & Freedom Movement, The Freedom and Rights Coalition and Voices for Freedom.
"The protest is a result of immense frustration and concern. People are outraged by the conduct of the government and its lack of respect, dismissive attitude and unwillingness to engage," the letter said.
"The position of protesters and the government have become entrenched, but this protest can end."
"Until the end of the mandates, participants are determined to maintain their presence," the letter said,
The letter also called for an "urgent meeting" with senior cabinet ministers to start a conversation.
On Monday, Prime Minister Jacinda Ardern flatly rejected the protesters' request for a meeting, pointing out some carried signs calling for the death of politicians.
National leader Christopher Luxon has backed the prime minister's decision.
But, ACT leader David Seymour today said he and ACT MP Nicole McKee met with a "couple dozen" people from the protest, and that he had passed a message to convoy leaders that it was time for a dialogue, but only if odious elements were removed from the protest.
Prime Minister Jacinda Ardern said it was irresponsible for the MPs to meet with the protesters, and National Party leader Christopher Luxon was similarly opposed.
In a statement on Wednesday evening, the Defence Force said: "Discussions on the possible deployment of NZDF assets remain ongoing and no decisions have been made.
"Four Army vehicles did travel today to the Wellington region from Linton and Waiouru.
"They are being pre-positioned should they be required, but as stated no decisions have been made about their use to assist the towing operation."
The Defence Force previously confirmed it had responded last week to a police request for assistance in removing vehicles blocking the streets in Wellington, but that discussions were ongoing.