Video report by ITV News Correspondent Paul Davies
Police in London have not "lost control" of the capital, according to Sadiq Khan, despite a surge in violent deaths.
The mayor denied claims that London was becoming "lawless", hours after one of its latest stabbing victims was named.
Israel Ogunsola, 18, was knifed to death in Hackney, east London, on Wednesday evening, the same week two other teenagers were fatally shot.
Mr Ogunsola's death is the latest in a spate of killings that has brought the number of suspected murders in the capital to more than 50 this year alone.
London's week of violence:
Thursday: Three youths, including two 15 year-olds, injured after being stabbed in Mile End; man in his 20s injured in Walthamstow stabbing; 13-year-old boy seriously injured after stabbing in Newham
Wednesday: Israel Ogunsola knifed in Hackney; man in his 50s dies outside Hackney bookmaker after suspected fight
Monday: Tanesha Melbourne, 17, shot dead in Tottenham; Amaan Shakoor, 16, shot dead in Walthamstow
Sunday: 20-year-old man stabbed to death outside club in Wandsworth
Mr Khan described himself on Twitter as "heartbroken" in the wake of the latest attacks.
The London mayor has found himself under renewed pressure this week to clamp down on the violent crime.
Stabbings in England and Wales are at their highest levels for years, with the situation particularly bad in the capital.
But Mr Khan denied that London was becoming "lawless", insisting to ITV News that he would be happy raising his family in the capital.
"We are a relatively safe city, but of course I understand the concerns people have when there are deaths caused by knives," he said.
Mr Khan criticised Government cuts to policing budgets, which have seen £700 million slashed over seven years, saying that there "has got to be a link" with the spike in violence.
"I don't accept the police have lost control," he said.
"What I do accept is there are less visible police - that's a direct consequence of police cuts.
"There are fewer police officers the public can see because there are fewer police officers."
Teenagers arrested over Ogunsola death
Mr Ogunsola was found injured in Link Street, Hackney, by police officers around 8pm.
He was pronounced dead 25 minutes later.
Scotland Yard later arrested two 17-year-olds on suspicion of murder.
The teenager's father, Dele Ogunsola, confirmed his son's identity on Thursday.
It was later reported that Mr Ogunsola was Facebook friends with Tanesha Melbourne, one of the victims of Monday's shootings.
Tanesha, 17, was shot from a car whilst she was with friends in Tottenham, north London.
That attack came 30 minutes before 16-year-old Amaan Shakoor was fatally shot in the face in Walthamstow.
'Worst I've seen it'
Labour's David Lammy, who has been MP for Tottenham for 18 years, described the violence on London's streets as the "worst I've ever seen it".
Speaking on BBC Radio 4's Today programme, Mr Lammy said there was "absolutely no sign" of any reduction in the violence as he raised concerns about drugs driving turf wars between gangs.
"I've had four deaths in the London Borough of Haringey since January, I've had as many knife attacks as there have been weeks in the year," he said.
"There are parents, friends, families, schools, traumatised and grieving, and there is absolutely no sign, I've got to tell you at the moment, of reduction in the violence."
Speaking at the scene of the Hackney stabbing, shadow home secretary Dianne Abbott blame the wave of bloodshed on cuts to policing and youth and social services.
She said: "It's really tragic, it's really horrible and mothers all over the capital must be thinking 'I can say goodbye to my son this morning but will he come back tonight?'
"Whether their son will turn out to be a victim or a perpetrator, it's traumatising for families.
"Here in Hackney we've lost one in 10 of our police officers since 2010, but there also needs to be more work done in youth work, in schools, even in mental health."
On Twitter, Liberal Democrats leader Sir Vince Cable called for the government to "address socioeconomic factors and provide adequate levels of funding for policing and protection on our streets".
Scotland Yard has blamed the rise in killings on social media.
Met Commissioner Cressida Dick said it was having a particular impact among children, where trivial disputes could escalate into violence "within minutes".
The Met says it is currently investigating 55 suspected murders since the start of 2018, including the deaths of two children whose bodies were found in Sussex.