Boris Johnson has been criticised by Nick Clegg for calling for "draconian" new laws to stop British people joining the Islamist terrorists of Islamic State, who murdered US journalist James Foley.
As well as calling for Foley's killer to be killed by a bomb, Mr Johnson said tougher measures should be introduced that would make travel to Iraq or Syria - without previously receiving the approval of authorities - a crime.
The deputy prime minister rejected these calls, telling the London Mayor: "I wish it were as simple as (Johnson) implies."
He said he would listen to what the police and intelligence services said they needed to tackle the "hateful ideology" of IS rather than accepting the Mayor of London's proposals.
Speaking during a visit to India, Mr Clegg said: "I think the issue is incredibly important, that we should make sure that those young men, and it is invariably young men, who are attracted to this hateful ideology that draws them to the bloodshed and conflict in places like Syria and Iraq, they shouldn't be able to come back and do harm on the streets of British towns, villages and cities, and that is now our number one priority.
"It's what the police, the authorities and security services are working flat out on; I have huge confidence in the outstanding work they do.
"With the greatest respect to Boris Johnson, I will listen to what they tell me they need rather than what he says.
"We actually have a number of measures already on the statute book which allow us to keep a very close eye on those people who aren't in prison, aren't sentenced, but nonetheless are perceived to be a threat to the United Kingdom.
"And of course, we will continue to review all the powers on the recommendation of the police and security services that may be deemed to be necessary to deal with this very serious issue."
He added: "I sometimes wish it was as simple as Boris Johnson implies: all we need to do is pass a law and everything will be well."
Intelligence agencies are close to identifying the brutal killer of US journalist James Foley, believed to be a British extremist who has been dubbed "jihadi John".
Mr Johnson said Britain must take on IS and "try to close it down now", warning that doing nothing would mean a "tide of terror will eventually lap at our own front door".
The mayor, who has overall responsibility for the Metropolitan Police, called for new laws that would mean anyone visiting Iraq and Syria would be automatically presumed to be terrorists unless they had notified the authorities in advance.
Writing in his Daily Telegraph column, Mr Johnson said: "Young men such as this killer are famously told that if they die in 'battle' they will be welcomed in heaven by the sexual ministrations of 72 virgins.
"Many of them believe it - even though scholars have suggested that the reference to 'black-eyed virgins' is in fact a promise of 72 raisins.
"I suspect most of us don't give a monkey's what happens to this prat in heaven, whether he meets virgins or raisins - we just want someone to come along with a bunker buster and effect an introduction as fast as possible."
Mr Johnson said those who "continue to give allegiance to a terrorist state" should lose their British status citizenship and called for swift changes to the law so there is a "rebuttable presumption" that those visiting war areas without notifying the authorities have done so for a terrorist purpose.
The mayor said that while Britain's recent military interventions have left the nation reluctant to wade into overseas conflicts "doing nothing is surely the worst of all" and warned that the IS "wackos" must be tackled.
"What is the point of having a defence budget, if we don't at least try to prevent the establishment of a terrorist 'caliphate' that is profoundly hostile to civilised values?"
But Richard Barrett, a former MI6 security chief, said the threat from IS was "unproven" and needed to be better understood.
The former global counter-terrorism director of MI6 told The Guardian: "This fundamental tenet of British justice should not be changed even in a minor way for this unproven threat - and it is an unproven threat at the moment."
He said the Government needed to understand better the domestic threat posed by IS before introducing new laws.
"I don't think we should change the laws without a very much more thorough assessment and understanding of the threat," he said.
"Sure, there's a problem with people who go to Syria and they may have broken the law if they joined organisations like Islamic State and al-Nusra Front, but there should be some sort of effort to prove that, rather than assume they've done so."
Former attorney general Dominic Grieve said Mr Johnson's suggestion that those travelling to Iraq and Syria should be presumed guilty was "draconian".
And he warned that calls to render suspects stateless by stripping them of British citizenship would mean tearing up a United Nations convention and could have a potentially damaging effect on the UK.
"It's entirely contrary to a United Nations convention of which we are signatories. The reason we signed up to it is because statelessness is a very real problem around the world," he told BBC Radio 4's World at One.
"I think the UK took the view that curbing statelessness was very important because, of course, if you render somebody stateless then another country may do the same thing to you in respect of its own nationals who happen to be situated in your country, leaving you with a major problem.
"So if we are about to rip up a UN convention, we need to think through the consequences."