Tony Blair wants to lower the age to 17 at which young people can receive long prison sentences for possessing a gun.
US-style surveillance of the homes of people suspected of possessing guns will also be considered.
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.
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.”