The family, who were living in Tokoroa, were travelling north and understood to be heading home at the time of the crash.
The children attended local schools, including Tokoroa High, Tokoroa Intermediate and Tokoroa North School.
The schools issued a joint statement this afternoon:
"There has been a tragic accident that has affected our whole community, in particular Tokoroa North School, Tokoroa Intermediate and Tokoroa High School.
"We can confirm students from our schools have been involved but we cannot confirm names as they have yet to be released by the police.
"We are currently putting support systems in place to support our staff, students and their whānau. This is our priority at this time."
Those close to the family have since been mourning their loss on social media, with many commenting of their shock on the couple's pages.
One told the Herald she was too distraught to speak, saying she was speechless but described them as a "mean [as] little big family".
Most of the children appear aged under 10.
Their deaths bring this month's road toll to 45 - the highest monthly death toll in 10 years.
Family have spoken of their sorrow on social media writing, "YOUS WILL ALWAYS BE IN OUR HEARTS .. MOST BEAUTIFUL FAMILY EVER !!!!!!!!!!!!!!", while another said "so sad my friend so sad this morning wish could go back to Saturday and start ur trip home again".
Another wrote "Shocked as .. R.I.P. with ya Babies cuzzies".
Grieving relatives were also gathering at a property trying to make sense of what happened. They declined to speak when approached for comment.
'Very nice people'
A neighbour of the family in Tokoroa, Ivan Meyers, 89, was distraught learning the family had died.
He described them as "very nice people and those kids too, were so polite, always a hello".
"They came here and I said 'seven kids, they will be noisy', but you couldn't get better behaved kids.
"They were good friends, nice people."
He had also just arranged for the 9-year-old boy to do his lawns so he could get some pocket money.
Colin Arnold, has lived in his Tokoroa home for 21 years, and described the family as "very caring".
"I found them, as neighbours, very warm and welcoming. The kids were also very friendly. The children imitated their mother in being warm and accepting. I would often see them playing on the front lawn with the neighbour's ginger cat.
"It was a wonderful family a lovely, caring mum and dad and what I couldn't get over was the beautiful manners that they had. They were great."
Meanwhile, Scouts NZ was last night supporting the family of the SUV driver, who had been with the organisation for many years.
Chief executive Joshua Tabor said the woman was travelling from Hamilton to Taupō after attending the closing dinner at the National Caving School in Waitomo on Saturday night.
She was scheduled to meet a senior volunteer before continuing to a work meeting in Palmerston North.
"We are committed to supporting her family as best we can given the sudden and tragic circumstances.
"We also extend our support and have offered counselling to our staff and volunteer community, many of whom worked closely with her during her long tenure with Scouts."