Mr Brown said he had spoken to Met chief Sir Ian Blair
Measures to tackle knife crime will be announced next week following recent stabbings in London and the Midlands, the prime minister has said.
Gordon Brown said the attacks - which are not linked - were "shocking and tragic". He promised a cross-government youth crime plan would be published.
On Thursday four men were stabbed to death in London and a fifth died after a stabbing in West Bromwich.
A man stabbed in north-west London on Friday remains critically ill.
In a written statement Mr Brown said he had spoken to Metropolitan Police commissioner Sir Ian Blair about the stabbings in London.
"I know the police are doing everything in their power to bring those responsible to justice," he said.
"The terrible stabbings that have occurred this week are shocking and tragic, and my thoughts are with the families and friends of those who have been hurt or killed in these attacks," he added.
He said the youth crime plan, which the government had been working on over recent months, would include new enforcement measures, improvements to sentencing.
A "new approach to youth crime prevention" would involve "tough parenting programmes targeted on areas with the most problems," he said.
"We will continue to make absolutely clear that carrying a knife is unacceptable in our society," he said.
On Thursday a 19-year-old was killed in an attack in Edmonton, north London, while two men in their 20s died a few miles away in Leyton and Walthamstow, east London.
A man aged 42 was found fatally wounded in Tottenham High Road, Tottenham, north London.
The day saw further fatal stabbings in West Bromwich in the West Midlands and Crosby, Merseyside. On Friday a man was wounded in north-west London.
He was left critically ill with wounds to his back and stomach after a stabbing in Brenthurst Road, Willesden.
Earlier Sir Ian said the recent spate of stabbings "graphically illustrates the need for everyone to pull together to put an end to this unacceptable violence".
Last year the Metropolitan Police recorded 160 homicides - about three every week. To have four fatal stabbings in one day could be a statistical freak, said BBC correspondent Andy Tighe.
Knife crime is mainly concentrated in Britain's cities and in London it has been falling, just as murder and manslaughter have also declined.
Metropolitan Police Assistant Commissioner Tim Godwin said: "I would hate anyone to think that all young people in London carry knives.
"We stopped 32,000 people in the main areas where we have concerns based on our intelligence. Out of those 32,000 searches, we've found 730 knives - so that's 2 in 100."
Home Office Minister Tony McNulty said there is a "stubborn residual of violent crime, including knives, around particularly some of our young people that is on an upward trend".
A Conservative Party spokeswoman said: "David Cameron outlined plans on Monday that would see a presumption to jail those caught carrying knives.
"This would upgrade the current system, which sees those caught with knives being let off with just a fine"
Criminologist Marian Fitzgerald told the BBC the police, politicians and the media only now seemed to be waking up to a problem which has been escalating since the mid-1990s.
"The fear is that the attention that it's now getting may almost be leading to a sort of copycat effect," she said.
Ms Fitzgerald - a visiting professor of Criminology at the University of Kent's Crime and Justice Centre - said this could be compounding what she called the "long-run rise in serious violence" in the UK.
'Greedy and rude'
Meanwhile, the government's advisor on behaviour in schools is preparing to outline a series of proposals on Monday, designed to put new pressure on parents to tackle children who behave badly.
Sir Alan Steer, headteacher of Seven Kings High School in Ilford, east London, said adults needed to set a better example if they want to halt the rise in gun and knife crime among teenagers.
"Sometimes as adults we don't model the behaviour we want youngsters to follow," he told The Guardian.
"We live in a greedy culture, we are rude to each other in the street. Children follow that."
Earlier this week Gordon Brown insisted ministers would take "any legislative measures" necessary to tackle knife crime.
The prime minister has argued that anyone over 16 caught with an illegal knife should be prosecuted, rather than escaping with a caution.