The US military is "reasonably certain" that the extremist Jihadi John was killed in an air strike aimed at the notorious British killer.
US military spokesman Colonel Steve Warren said it would take "some time" to confirm the death of the extremist - real name Mohammed Emwazi - who was targeted in the Syrian stronghold of Islamic State (IS).
David Cameron has hailed the apparent death of Jihadi John as a "strike at the heart" of the extremist group.
But Labour leader Jeremy Corbyn said it would have been "far better" if Emwazi had been brought to justice in the courts for his "callous and brutal crimes".
Col Warren, the spokesman for the operation tackling IS, told reporters it was not an "exact science" but the intelligence gave the US "great confidence" that the individual targeted was indeed Emwazi, who he described as the "face" of IS.
"Now we are using the same intelligence capabilities to verify that the individual we killed was in fact Jihadi John," Col Warren said.
The "high value individual (HVI)" is believed to have been killed along with an associate - or "worst best friend" - who may have been the driver of the car they were in when it was attacked with a Hellfire missile fired from a drone.
Speaking from Baghdad, Col Warren said: "For us it was a fairly routine HVI strike."
Although Emwazi was not thought to be a major tactical figure within the ranks of IS his appearance in a series of videos apparently showing the brutal murder of several hostages including Britons Alan Henning and David Haines meant he had propaganda value for the extremist group.
Col Warren said: "Jihadi John was somewhat of an Isil celebrity, if you will, kind of the face of the organisation in many senses. So there is certainly a significant blow to the prestige of Isil.
"But Jihadi John was not a major tactical figure or an operational figure."
Col Warren described Emwazi as a "human animal" and "killing him is probably making the world a little bit better place".
The Prime Minister said the US drone attack targeting Emwazi was an "act of self-defence" and "the right thing to do".
He was backed by the chairman of the Intelligence and Security Committee (ISC), who said there was a "sound legal basis" for the air strike in the Syrian stronghold of the terror group, which is also known as Isil or Daesh.
In a statement delivered outside 10 Downing Street, Mr Cameron stressed it was not yet absolutely certain that the "barbaric murderer" was dead.
"If this strike was successful - and we still await confirmation of that - it will be a strike at the heart of Isil," he said. "And it will demonstrate to those who would do Britain, our people and our allies harm, we have a long reach, we have an unwavering determination, and we never forget our citizens.
"Britain and our allies will not rest until we have defeated this evil terrorist death cult and the poisonous ideology on which it feeds."
He said Britain had been working "hand in glove" round the clock with its closest ally, the US, to track down and target the militant, who is believed to be responsible for the deaths of several IS hostages, including Britons Alan Henning and David Haines.
He argued that Emwazi had remained a threat to innocent people, including in the UK.
"This was an act of self -defence. It was the right thing to do," he said.
The air strike targeting Emwazi was carried out in Raqqa, the IS stronghold in Syria, last night.
Mr Corbyn said in a statement: "We await identification of the person targeted in last night's US air attack in Syria.
"It appears Mohammed Emwazi has been held to account for his callous and brutal crimes. However, it would have been far better for us all if he had been held to account in a court of law.
"These events only underline the necessity of accelerating international efforts, under the auspices of the UN, to bring an end to the Syrian conflict as part of a comprehensive regional settlement."
ISC chairman Dominic Grieve told BBC Radio 4's World At One: "It's always better if somebody is guilty of a serious crime that they should be brought to justice through the ordinary legal process but in this case it was clearly impossible for that to happen.
"On the basis that he has been targeted, there is sound legal base for targeting somebody who poses such a risk to other people and has proclaimed himself as willing to kill them."
Mr Grieve, a Tory MP, said his cross-party watchdog would be meeting soon and "may well" extend its inquiry into a previous UK drone strike in Syria to cover this operation.
"The ISC has indicated it is interested in looking at the intelligence base on which strikes take place," he said.
"Whether a strike takes place directly by the UK or indirectly, where we are helping a strike by the US, doesn't really make any difference to the legalities - we are still involved.
"You cannot use a strike as an act of retribution but you can use it as legitimate self-defence.
"If a person is threatening people and is outside the ordinary justice system because you cannot bring them to account or stop their activities then there is a legitimate base, I think it is widely recognised as such."