David Cameron has hailed the apparent death of "Jihadi John" as a "strike at the heart" of Islamic State (IS).
The Prime Minister said the US drone attack targeting the notorious British killer - real name Mohammed 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.
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".
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.
Pentagon press secretary Peter Cook confirmed that US forces carried out an air strike in Raqqa last night "targeting Mohamed Emwazi, also known as Jihadi John".
He said: "We are assessing the results of (the) operation and will provide additional information as and where appropriate."
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."