Tony Blair wants to lower the age to 17 at which young people can receive long prison sentences for possessing a gun.
Announcing a firearms law review, he said he was considering lowering the age from 21 for a mandatory five-year jail term for carrying a gun.
He told the BBC he was also considering criminalising gang membership and how to protect people giving evidence.
But he insisted that gun crime was "a specific problem within a specific criminal culture".
He was speaking after four fatal shootings in London this month.
Three of them were teenagers shot dead in south London - two of them in their own homes.
And on Saturday, a 28-year-old man was shot dead in Hackney, east London, while three men are still in hospital after being shot in two separate attacks in the Moss Side and Longsight areas of Manchester.
The prime minister has called a summit of ministers and the police this week to talk about how to challenge gun violence.
But speaking on BBC One's Sunday AM programme he argued gun violence was not a "general state of British society" and "British young people".
The number of people injured by firearms in England and Wales has more than doubled since 1998
In 2005/2006, the number of gun murders fell by more than a third from 78 to 50
There were 11,084 recorded firearms crimes in 2005/2006 - up 0.12% on previous year
London, Greater Manchester and the West Midlands account for 54% of recorded incidents
Source: Home Office
"It is about a specific problem within a specific criminal culture to do with guns and gangs, which doesn't make it any less serious, incidentally, but I think it's important therefore that we address that actual issue."
He said it was about looking at how to "clamp down" on those young people who get into gangs at an early age and use guns.
Mr Blair said US-style surveillance of the homes of people suspected of possessing guns or trading in them will also be considered.
Mr Blair denied the announcements were a "knee-jerk response" to the recent killings.
And he said it was important to highlight that overall there was some good news on crime and in particular gun crime.
Shadow home secretary David Davis welcomed the review, but warned: "Yet again we are seeing the prime minister reacting to a headline rather than dealing with the issues in the long-term.
"We now have to think what are they going to do for 16-year-olds and 15-year-olds because these gangs won't stop at using younger kids to carry guns, drugs, whatever it may be."
He told Sky News's Sunday Live: "We have got to take some time. Think it through, do it properly."
Lib Dem leader Sir Menzies Campbell said there were "no quick fixes" to the problem.
"Rather than new laws we need more police and more effective policing," he told BBC News.
"All young people should feel they have a stake in society - effective schooling, more engaged youth services and better community support are all needed to help young people escape the cycle of deprivation and gang culture."
In Hackney, the victim was shot as he got out of a car outside a restaurant in Homerton High Street in the early hours of Saturday. He was pronounced dead at hospital.
On Wednesday, Billy Cox, 15, of Clapham, died from a gunshot wound to the chest, a post-mortem examination has said.
His shooting followed the deaths of James Andre Smartt-Ford, 16, and Michael Dosunmu, 15, who were gunned down in Streatham and Peckham respectively.
One 18-year-old gang member from Moss Side, known to friends as Frank, told the BBC's Mark Simpson what he thought of Mr Blair's plans for tougher gun laws.
Wearing a bullet-proof vest because he said shootings had become so random, he felt he had a "50-50 chance" of being shot.
Asked if a longer sentence would be a deterrent, he said: "Yeah, it probably will, but it's not going to stop it."
He believed the gangs were trapped in a "vicious circle" of tit-for-tat shootings.
Norman Brennan, director of the Victims of Crime Trust, said: "If you tell them they're going to spend 20, 30 or 40 years in prison, what difference does that mean to a young offender armed with a gun who has no value for life?
"These youngsters will live by the gun and die by the gun. These are walking assassins and walking assassins never care about the sentence they are going to get."