Almost 400 people have contacted the inquiry set up to examine child abuse in Catholic and state-run homes in Northern Ireland.
Among those who have already come forward are people from Australia.
They were contacted by a team of experts who travelled to the country to speak with potential witnesses who had been transferred from institutions in Northern Ireland, as part of the government's child migration scheme.
The inquiry is due to report to the Executive in 2016, however people who wish to take part must submit a formal application by 29 November.
Patrick Corrigan, from Amnesty International, said there is a demand for people to have their stories heard.
He said: "We knew there was a demand when we campaigned, alongside victims, for this inquiry.
"We knew there were scores of victims because that's how many we were working with, but now that hundreds have come forward, it really has underlined the fact this was needed and that their stories deserve to be heard and this inquiry is giving them that chance."
Hopefully this will give the victim some peace of mind and that you don't have to carry the hurts and pains and this baggage around with you for the rest of your days.
Margaret McGuckin, from the victims' group Survivors and Victims of Institutional Abuse (SAVIA), said the inquiry would give victims the opportunity to have their story heard for the first time.
She said: "This could be the last time ever that their stories could be heard.
"In many cases it has been 60 years or more since the abuse took place and there are many people who have not lived to see this day.
"And we would encourage everybody to come forward."
She continued: "I know of so many who have taken their own lives and died through alcohol and drug abuse because they have never been able to tell anyone about the abuse they suffered.
"There have been other investigations that have gotten nowhere because people couldn't talk.
"But now is the time."
Mr Corrigan added: "Hopefully what will come from this will be truth, acknowledgement of what was done, both by the institutions and by wider society and justice."