Speaking at his regular Downing Street press conference, the Prime Minister insisted that those carrying knives were more likely to be caught and face punishment now than ever before.
But he admitted: "Too many people, young and old, do not feel safe in the streets, and sometimes even in their homes, as a result of the behaviour of a minority.
"We need to make it absolutely clear to everyone, but especially young people, that in our country there are boundaries of acceptable behaviour, that it is completely unacceptable to carry a knife."
He went on to say that there were more stop-and-searches being carried out than ever and more cash for such procedures.
A new presumption to prosecute offenders also meant they were ever more likely to be punished.
He said community sentences were being strengthened to make them "tough, visible and effective" and that the Government would do more to prevent youngsters "falling into crime".
Early intervention would be extended to 20,000 families, who would face the threat of eviction if they failed to respond positively to support.
Mr Brown said crime was down by a third and the number of police on the street dramatically up - but there was still a "huge amount" to do.
"I accept that as long as young people, or any person, feels unsafe in our streets and our neighbourhoods the job is not done and a huge amount is still to be done. And that's why we are toughening up punishment, toughening up enforcement and toughening up prevention," he told reporters.
Asked why he would not simply promise to lock up all those carrying knives, he said: "When someone is carrying and using a knife there is absolutely no doubt that they should go to prison.
"But I notice those people who were proposing prison simply for there being a knife have drawn back from that and talk about a presumption of prison and about the different kinds of knives that would be exempted.
"What I want to see is anybody who is using a knife goes to prison; anybody who is carrying a knife is subject to either prison or a strong community payback that forces them to give service to the community.
"These are the types of sentences that young people must know will be applied against them."
Mr Brown criticised advice to magistrates from the Sentencing Guidelines Council that possession of a knife could be punished with just a fine.
He said: "What the sentencing council has said is not acceptable to me."
But he said that, in the case of a 14-year-old caught with a knife for the first time, it might be "inappropriate" to send them to jail or a young offenders' institution.
"What we should do is say to them 'There is a presumption to prosecute, you will be punished'. We are absolutely clear that that punishment will be severe.
"That punishment will include going to prison or tough community payback."
He said such offenders could face up to 300 hours of unpaid work, with tasks set by communities, such as cleaning graffiti and tending parks on Friday and Saturday nights.
The Government would also be focusing on the one in 20 young people responsible for half of all youth crime, he said.
"These are the families whose children are disrupting the classrooms and roaming the streets committing crime," he said, promising increased support but "tough sanctions" for those who do not respond.
Mr Brown said there were 110,000 families in need of support where children were at risk of becoming prolific offenders.
Early intervention would take place in about 20,000 families, where, he said, "it's clear that the mother or father have lost control of their children and their whole life is actually in difficulty".
The rising tide of knife violence
Police and ministers have been stunned by a spate of knife murders in London and other major cities this year.
Five people were killed in as many days in the capital last week, with fatal stabbings also taking place in West Bromwich in the West Midlands and in Crosby on Merseyside.
The grim toll grew over the weekend with Paul Gilligan, who was in his thirties, stabbed to death in a pub in Bolton early yesterday. It was the third knifing in the town in just 48 hours.
Another man died yesterday after being stabbed in the head and chest during a disturbance in Withywood, Bristol. Two men were last night being questioned over the incident.
A 22-year-old concert-goer, meanwhile, is critically ill after being found with multiple stab wounds in the campsite of the T in the Park music festival in Perthshire in the early hours of yesterday morning. Police were last night continuing to hunt for two men in connection with the "horrific" stabbing .
In Redcar, Cleveland, a 21-year-old man had surgery after a knife attack. The unnamed man was taken to James Cook University Hospital in Middlesbrough for treatment following the incident in Dormanstown. Cleveland Police said that a 21-year-old woman had been arrested and remains in custody. In South Shields, Tyneside, a man in his forties was in a stable condition in hospital after being stabbed a number of times. A Northumbria Police spokesman said that a 37-year-old woman was arrested at the same address.
