The group say they have continued with their case because of their concern for the wellbeing and welfare of children.
Addressing the court today, the group's lawyer, David Jones, said the Government's decision-making must be questioned.
"When one has the government bodies who are charged with making decisions that can affect young people, we have a situation where that must be given the closest scrutiny," he said.
"Government agencies tend to say they got it right and continue to say they got it right - but it doesn't mean they are right".
Jones said the Government's process to approve the vaccine was rushed and an "absence of data" of the effects on people who were going to be vaccinated was "concerning".
"It is concerning that known issues with the mRNA technology and also the information that is being promoted and the information that is being withheld in some ways."
He claimed the Government's statements that it cut no corners in the consideration for the vaccine rollout "are simply incorrect".
The group referenced the work of Dr Robert Malone in the hearing - an American who is vaccinated himself, helped invent mRNA vaccines, but whose claims of vaccine side effects have been long and widely disputed by the international community.
Jones said that evidence shows "healthy children do not need synthetic product to protect themselves from Covid-19" to which Justice Warwick Gendall asked: "what about unhealthy children?"
Jones referred to the ways in which children who were unhealthy could be protected from the virus, such as isolation.
"But if you're going to have a vaccine which could compromise the health of healthy children, then it should be further away as far as unhealthy children are concerned," he said.
Nearing the end of the day of evidence from the applicants, Crown lawyers, representing the Minister of Health, were able to respond to some of the claims today.
Lawyer Kate Weaver said that there has been plenty of time dedicated to a robust consideration of the rollout by the Crown.
She said the Government had a responsibility to treat the rollout with urgency, as it was dealing with the Delta outbreak.
"Fortunately for the vast majority of children, [Covid-19] is a mild illness, and the Crown does not dispute that, and all of the documents make that clear - but it can cause severe disease in children, including in healthy children," Weaver said.
Responding to Jones' comments on unhealthy children's protections - being isolation - Weaver said that was a wholly unacceptable approach for the Government to take.
"Children who are at high risk for whatever reason, their parents should have the option of choosing to vaccinate their child rather to have to keep them at home."
The Crown said there clearly was a high need for the rollout and the decision was an urgent matter.
Citing a report that was considered by Medsafe and previously presented to the Waitangi Tribunal, the Crown argued stopping the rollout would disproportionately impact Māori and Pacific children.
The report highlighted Māori and Pacific children, much like adults of the same ethnicity, were disproportionately at risk of contracting the virus, and experienced worse health outcomes compared with other children.
The court proceedings will continue tomorrow.
