Voller delivered the message via his lawyer on the day terms of reference were announced for a royal commission into the juvenile justice system in the Northern Territory.
The North Australian Aboriginal Justice Agency (NAAJA), which has represented many of the youths, has called for Don Dale's High Security Unit to be closed immediately.
"It is a barbaric and draconian facility which has no place in a justice centre" NAAJA senior youth lawyer Jared Sharp said.
The ABC's Four Corners program on Monday night documented the physical and emotional abuse of Dylan Voller and other teenage boys in the NT's corrections system since 2010.
Images of Voller strapped to a chair while hooded were among the most confronting broadcast on the program, which has gained international attention.
A former youth detention worker this week claimed Voller had been put in the restraint chair on at least three occasions — once when he was under 13 years old.
Voller is serving almost four years jail for attempted robbery, aggravated robbery and recklessly endangering serious harm. He is due for release in October 2017.
Former NT chief justice Brian Ross Martin will head the Royal Commission, which will examine child protection and youth detention over the past decade, look at what violates were committed, what safeguards were in place and if the Northern Territory Government did enough to address issues in the system.
"The royal commission will conduct a thorough and thoroughly independent inquiry into the specific systemic problems identified within the Northern Territory, how those problems arose, the failure to identify and correct them, and appropriate reforms," Prime Minister Malcolm Turnbull said.
Pressure has been growing on NT Chief Minister Adam Giles to explain his Government's lack of action.
Details of the abuse have been public in the Territory for at least the last two years.
Giles says Government has 'taken responsibility'
Speaking in support of the royal commission on Thursday, Mr Giles softened his rhetoric on young offenders.
"I want to get to the bottom of identifying if there are other youth detainees who have suffered injustices in the system," he told ABC local radio in Alice Springs.
But he would not meet Voller's request.
When asked if he was prepared to provide Voller and other inmates with a personal apology, the Chief Minister said: "I'm sorry that there are too many kids that find their way into the child protection system."
Later in an interview with 7.30, Mr Giles said his Government had "taken responsibility" for the situation in the juvenile detention centre.
"Certainly since we saw the Four Corners report, we moved very quickly to seek to establish a royal commission," he said.
"It's great to be working with both Malcolm Turnbull and George Brandis in how we can jointly run that royal commission."