Downing Street has labelled a claim MI5 may have contributed to the radicalisation of Mohammed Emwazi, known as "Jihadi John", as "reprehensible".
A Number 10 spokeswoman told a Westminster briefing: "It is completely reprehensible to suggest that anyone who carries out such brutal murders - they are the ones responsible and we should not be seeking to put blame on other people, particularly those who are working to keep British citizens safe.
"The people responsible for these murders are the people that we have seen in the videos."
Asked whether Mr Cameron shared the view of murdered British aid worker David Haines's daughter, Bethany, who said victims' families would feel closure only "once there's a bullet between his [Emwazi's] eyes", the spokeswoman replied: "The Prime Minister wants to see the murderers brought to justice."
The west London man named as Islamic State killer "Jihadi John" claimed he had been warned five years ago that MI5 would be keeping a "close eye" on him, the Guardian reports.
In transcripts of Mohammed Emwazi's first interview with advocacy group Cage, the former Westminster student said an MI5 handler told him, despite claims to the contrary: "I still believe you are going to Somalia to train."
According to the report, Emwazi also said the agent "threatened" him, and claimed: “We are going to keep a close eye on you, Mohammed, and we already have been … We are going to keep a close eye on you.”
He also said he was asked his views on the 7 July and 11 September terror attacks on London and New York, and claimed he had replied that they were "wrong", adding: "If I had the opportunity, would I make those lives come back? I would make those lives come back."
It is unclear whether the claims made in the interview are true.
Mohammed Emwazi, the British graduate named as Islamic State murderer "Jihadi John", was a model worker who was "very good with people", his former employer has said.
The manager of an unnamed IT firm that hired Emwazi as a salesman while he lived in the Gulf told the Guardian he was "the best employee we ever had".
"How could someone as calm and quiet as him become like the man who we saw on the news? It's just not logical that he could be this guy," he said.
"I have no answers for this. He wasn't sociable. He was always earnest. He didn't smile. But he wasn't bad."
He said Emwazi had left the company when he returned to England in 2010, adding: "Maybe he fell into the wrong hands when he went back."
Home Secretary Theresa May said the threat to the UK faces from terrorism is "grave and growing". She was responding to an urgent question in the House of Commons from Labour's Yvette Cooper.
Ms May reiterated the government's advice against British citizens travelling to Iraq and Syria.
She said the government has "consistently and emphatically advised against any and all travel to Iraq and Syria and when this happens we have seen that the impact on families and communities is devastating".
She added that all aspects of society must play their part to fight against radicalisation.
Shadow Home Secretary Yvette Cooper will ask an urgent question on Government counter terrorism policy at 3.30pm in the House of Commons.
The question is also expected to raise the issue of the implications for UK individuals travelling to conflict zones in Syria and Iraq.
The Prime Minister has vowed to do "whatever it takes" to protect the UK from extremists - and said he wants to work with technology companies to lock down loopholes which can be exploited by terrorist groups.
Speaking at an event in Colchester, David Cameron said he had concerns over the way groups such as Islamic State might be able to communicate in future - and said more laws might be needed.
My view is national security comes first. Whatever it takes, whatever is necessary to keep the British public safe, I will always be a Prime Minister who wants to push for those changes.
Over time, yes of course, we are going to do more to make sure that as technology develops we can make sure we can keep people safe.
I'm not satisfied that we can allow means of communication to develop which in extremis we are simply unable to intercept.
That is the concern I have and I have said that many times before.
A government review will look into the connection between three young men who went on to become jihadist fighters after attending a London school.
Former pupil at Quintin Kynaston academy, Mohammed Emwazi, has been revealed to be the man behind the mask of a violent extremist known as Jihadi John, who appeared in a number of propaganda videos in which he murdered Western hostages.
Meanwhile, two other alumni of the school - Choukri Ellekhlifi and Mohammed Sakr - both died in combat in 2013 after joining militant Islamist groups Al Qaeda and al-Shabaab, raising fears the boys may all have been radicalised as teenagers.
Former head at the school, Jo Suter, denied that teachers knew anything about the boys being radicalised, while a Department for Education spokesman said the ability of authorities to monitor possible radicalisation in schools had "advanced hugely" in recent years.
The DfE... [is] working tirelessly to develop our understanding of the problem and to see if and where we can offer help to schools with pupils or former pupils who have since travelled to Syria or other areas of concern.
The Secretary of State has asked them to review those schools where we have evidence of links with pupils who have travelled to Syria. The allegations about Quintin Kynaston may be historic and it is clearly a completely different school today, but I'm sure we will look back at the evidence from the time as part of this review to see if there are any lessons we can learn for the future.