An international manhunt is under way for the jihadist, believed to be British, who appeared in video footage showing the beheading of American journalist James Foley.
Police are analysing footage of Mr Foley's death for clues amid suggestions that the Islamic State (Isis) extremist - who has been reportedly identified by a former hostage as "John" - is from London. The FBI is leading the search for the killer.
Didier François, a former hostage who was released by Isis in April, told Europe 1 Radio he had some idea of who the killer could be.
According to a translation by The Telegraph, the 53-year-old French journalist said: “Recognised is a very big word. I see roughly who it is.”
Mr François said he had been held with Mr Foley from last August until April and that he was also held almost nine months with fellow journalist Steven Sotloff.
"He [Foley] was an extraordinary person with a strong character. He was a pleasant companion in detention because he was solid and collective. He never gave in to the pressure and violence of the kidnappers," Mr François added.
He had not spoken of Mr Foley and Mr Sotloff until now because he was warned upon his release that if he told the public he had been held with them, reprisals would follow against them.
He said: "Their exact words were: ‘They’ll be punished’.”
In a separate interview, he told Reuters he believed Mr Foley was under the control of Isis or its affiliates the entire time.
"The guy who killed him is the guy who took him from the start."
He said Mr Foley had been singled out and subjected to extra beatings because his captors had discovered pictures of his brother, who works for the US Air Force.
Nicolas Hénin, an independent reporter who was also taken captive by Isis, told L’Express magazine Mr Foley became “the whipping boy of jailors”.
"Because of that and as he was American, he got extra bad treatment. He became the whipping boy of the jailers but he remained implacable," Mr Henin said.
Another former hostage, who was held for a year in the Syrian town of Raqqa, told The Guardian the killer was the ringleader of a trio of UK-born extremists the captives nicknamed "The Beatles" because of their nationality.
The Guardian's Martin Chulov told Sky News: "We spoke to a hostage today who was released several months ago and he clearly identified to us this man in the video.
The hostage said the fighter was "the leader of the pack, someone who was very assertive and was responsible for negotiations with hostage families and certainly had spoken to many mums, dads, (and) wives on Skype".
Richard Barrett, the former MI6 director of global counter-terrorism, told BBC Radio 4's Today programme tracing the killer is possible, but there would be “huge problems involved” with bringing him to justice.
Shiraz Maher, a senior researcher at the International Centre for the Study of Radicalization at King's College London, said Mr Foley's death was evidence that British jihadis were "some of the most vicious and vociferous fighters" in the Middle East and “very much at the forefront of this conflict” with roles ranging from suicide bombers to executioners.
Earlier today, US officials confirmed that a Special Operations mission tried and failed to free Mr Foley and other hostages in Syria weeks before he was murdered by militants.
The White House and Pentagon released statements yesterday confirming that President Barack Obama personally authorised the July raid on an oil refinery in northern Syria.
The mission failed because the hostages, thought to have been held there in the weeks leading up to the operation, had recently been moved.
The British Prime Minister, David Cameron, and Mr Obama have condemned the murder of Mr Foley as "hateful" and "barbaric", insisting it would not force them to back away from tackling Isis in Iraq and Syria.
Mr Cameron, who has since resumed his holiday in Cornwall after returning to Downing Street when the video surfaced, said it seemed "increasingly likely" that the killer was a UK citizen.
"Let's be clear what this act is - it is an act of murder, and murder without any justification," Mr Cameron told reporters at No 10.
Mr Obama said "no just God" could condone the killing of Mr Foley, who was seized in Syria in 2012, and Isis would "fail" because they only wanted to destroy.
The murdered journalist's younger brother Michael criticised the American government, saying he thought it could have done more to save him.
One of the agencies Mr Foley worked for,GlobalPost, has said Isis threatened to execute him a week ago and the US authorities were informed.
The film shows Mr Foley, 40, who worked for organisations including Agence France-Presse and went missing in Syria in 2012, kneeling in a desert-like environment at an unknown location as an Isis fighter stands by his side dressed in black and with his face covered.
The footage has been authenticated by the US and UK, but Scotland Yard has urged people to avoid spreading it through Twitter and Facebook - warning that to do so could be a criminal offence.
The US is thought to be considering an additional deployment of troops to Iraq to help repel the Isis offensive that has secured swathes of the country.
But Mr Cameron stressed there would be no "knee jerk" escalation of British military involvement - warning that the West faced a "generational struggle" against Islamist extremism.
"I have been very clear that this country is not going to get involved in another Iraq war. We are not putting combat troops, combat boots on the ground, that is not something we should do."
Additional reporting by agencies