The families of stabbing victims are calling for a five-year minimum sentence for carrying a knife.
Jayne Walmsley's son, Luke, was stabbed to death at school
The petition, backed by the parents of Luke Walmsley and Damilola Taylor, was handed to 10 Downing Street on Monday.
Paul Walmsley, whose 14-year-old son was killed at school, said those caught with knives should "serve some form of term in youth custody or in a prison".
The families are backed by the Victims of Crime Trust, which says a child dies in a knife attack every two weeks.
It says there are three times as many fatal stabbings as gun deaths and penalties for carrying a knife should be the same as for carrying a gun.
The Knives Destroy Lives campaign is calling for a five-year minimum jail term for carrying a blade longer than three inches.
It wants a six-month minimum jail term for carrying a blade
shorter than three inches, or three months in the case of juveniles.
Jayne Walmsley, whose son died last November, said the government had been too slow to tackle knife crime.
The parents of Damilola Taylor, who was 10 when he died in Peckham, London, in 2000, were not at the campaign launch.
But his father, Richard, earlier said that current knife laws have "no effect at all" and it was time for ministers to realise "enough was enough".
Supporters also included Michael Hegarty, whose brother Bernard was stabbed in east London in August, while on his lunch break.
"It's a mad world out there. Things do need to be addressed," said Mr Hegarty.
Antoinette Rodney, whose 15-year-old son Kieran Rodney-Davis was stabbed for his phone, said: "It's getting worse and we've got to do something about it. "
Home Secretary David Blunkett is meeting police on Wednesday to discuss ways of tackling knife crime.
He is considering raising the minimum age for buying a knife to 18.
Chairman of the home affairs select committee, John Denham, was reluctant to endorse a mandatory sentence, saying that courts needed to have some discretion.
However, he called for a higher maximum penalty as well as increased use of "restrictions on liberty", such as electronic tagging and curfews.
"The problem with knives... is that the top penalty of two years' imprisonment doesn't send a strong enough message and no one really gets it," he told Today.
"But secondly, other parts of the system are failing.
"We have too many schools, for example, who confiscate knives rather than routinely involving the police and making sure the carriers are charged."