The Green Party said it backs the call for an inquiry and formal apology.
"It seems everyone but the Government realises that an inquiry and a formal apology are essential to helping the victims find some sense of closure, and to ensure that children in state care now and in the future are protected from abuse," said the party's social development spokeswoman, Jan Logie.
"The Minister for Social Development [Anne Tolley] needs to issue a full universal apology to those abused while in state care, and immediately set up an independent body to resolve historic and current complaints of abuse and neglect.
"Bill English is happy for things to remain unknown and unexamined around the abuse of children in state care."
English told Radio New Zealand that he hadn't yet seen the details of the open letter, but he noted much work had been done regarding abuse claims - the confidential listening service headed by Henwood and a process of settling claims with compensation and an apology.
"The question would be, would an inquiry add anything."
Asked if he didn't want to know the extent of the historic abuse, English said, "I think the extent of it is pretty well known and pretty well understood."
The real challenge was to find effective ways for the state to care for children and the Government's systems of care were going through major changes to make sure the abuse that occurred in the past did not happen again.
He said implementing these changes was a higher priority than holding the kind of large, long-term, complex inquiry the Human Rights Commission seemed to envisage.
Maori Party co-leader Marama Fox said: "We absolutely support the commission's call for those who haven't been able to share their stories, to do so.
"This Government needs to listen to them and learn from them so that abuse never happens again."
"I've heard the stories from people themselves, who as children were taken from homes that were actually more loving than the ones the state put them in. They are New Zealand's lost generations."
The party's other co-leader, Te Ururoa Flavell, said the country's "lost generations" issue was more serious than most people thought.
"We're potentially talking about thousands of children being taken from their families simply for having a disability, being Maori or minor transgressions like skipping school, only to be abused physically, sexually and emotionally by the strangers and institutions that the state placed them with."
Ken Clearwater, the manager of the Male Survivors of Sexual Abuse Trust, said it first approached then-prime minister Helen Clark in 2004 for a Royal Commission into the institutional abuse of children.
"This was denied as was an approach to John Key and the National Government.
"We have sent several letters over the years and continue to ask Minister Anne Tolley.
"Why an Inquiry? For Government and the public of New Zealand to see the horrendous sexual physical and emotional abuse suffered by vulnerable children at the hands of those who were supposed to care for them.
"This goes not just to state care but also abuse suffered while in church and other institutions. Many victims ended up in the mental health or prison system and many are still in either of these systems or on some kind of benefit."
"An Inquiry or Royal Commission is important for all those affected to be heard and helped. Systems need to be set up for long time care. The many things the victims missed out on, education, health and mental health, accommodation and help into work.
"Giving someone $12,000, an apology and then sending them on their way is an insult not an answer, and is not right for all.
"Judge Henwood, who was in charge of the Confidential Listening and Assistance Service, has asked for a public inquiry. In her report you will see that many gangs in NZ were formed out of state care."
• To view the open letter and petition: neveragain.co.nz