The inquiry was thrown into crisis this week following the resignation of its chair, Susan O’Brien, who quit just days after fellow panel member Professor Michael Lamb.
Survivors’ groups met Mr Swinney in Edinburgh today to discuss the inquiry, and said their discussions had been “productive”.
Campaigners want the Scottish Government to extend the inquiry to include children abused by those who had a duty of care, not just those who were abused in institutional settings.
There are also growing calls for the new chair to be appointed from outside of Scotland, with leading barrister Michael Mansfield QC already approached by survivors’ groups.
Speaking after today’s meeting, Alan Draper, parliamentary liaison officer for In-Care Abuse Survivors (Incas), said: ““The view around the table was that the remit needs to change. It needs to take into account the many survivors who are wondering why they are not included in this inquiry.
“I remain suspicious of the government, but I am happy that John Swinney today has attempted to re-assure us the best he can.”
David Whelan, who represents former Quarriers residents, said: “We’re committed to continuing to work with the government to resolve the issues and work is ongoing.
“I’ve been doing this for 18 years since my abuser was convicted. Survivors are waiting for compensation, they’re waiting for support mechanisms. This has gone on for too long. Scotland has to face up to its responsibilities.
“The deputy first minister has given us reassurances, but we’ll wait and see the outcomes. We’ve been let down in the past.”
Mr Whelan said Mr Swinney had been asked to look at widening the inquiry’s remit.
“These paedophiles and these abusers not only worked in these institutions, they worked in the Boy Scouts etc,” he said.
“We told the minister you need to make sure children are safe in this country - you need to look at every institution, not just care homes.”