The 43-year-old British photojournalist, who has been held captive for more than two years, appeared in the fifth episode of propaganda films entitled Lend Me Your Ears.
Its release came just days after his father Paul Cantlie, 80, died from complications following pneumonia.
As in previous instalments, he can be seen delivering his message under duress from behind a desk, wearing an orange jumpsuit and criticising the British and American governments.
In the apparently scripted footage, which lasts six and a half minutes, he said: “Now, unless we tried something stupid like escaping or doing something we shouldn’t, we were treated well by the Islamic State.
“Some of us who tried to escape were waterboarded by our captors, as Muslim prisoners are waterboarded by their American captors.”
He read from e-mails allegedly exchanged between IS and the families of American captives who complained about the US government’s refusal to negotiate their loved ones’ release.
One message, which Mr Cantlie dated to 17 July this year, reads: “We have begged them so many times already. Everyone has buried their heads in the sand. We feel we are caught in the middle between you and the US government, and we are being punished.”
Mr Cantlie’s sister, Jessica Cantlie, has previously appealed for there to be “direct contact” with the militants holding him.
In his latest statement, Mr Cantlie made no reference to recent events and it is not clear when the footage was filmed.
He is reported to have written on the group’s English-language online propaganda site that he had recorded eight episodes which would be released one by one.
Mr Cantlie, who has worked for newspapers including the Sunday Telegraph and the Sunday Times, signed off by saying that in the next instalment he will talk about a failed rescue mission.
He said he will explain how “one soldier was worth five prisoners and we were worth none”, in apparent reference to the deal the US government made with Taleban fighters to free Sergeant Bowe Bergdahl in exchange for five detainees at Guantanamo Bay.
Since August, IS has filmed and posted online the deaths of four Western hostages.
UK aid workers Alan Henning and David Haines, and American journalists James Foley and Steven Sotloff were beheaded on camera by the jihadi organisation, which is also known as Isis and Isil.
A fourth jihadist fighter from the UK has been killed in Syria, according to reports yesterday.
He was said to be Mehdi Hassan, 19, from Portsmouth, Hampshire, who travelled to the country with a group of four other men in October last year.
Chairman of the Portsmouth Jami Mosque, Abdul Jalil, said: “It has been confirmed with the family that he has died.”