The comment came less than a week after 14-year-old Mohammed Ahmed Hussain was recovering from being stabbed in the stomach outside Heartlands high school, in Birmingham.
Three teenagers were arrested on suspicion of murder and have since been released on police bail.
The incident followed the stabbing of talented footballer Kiyan Prince, 15, who was knifed to death outside the London academy in Edgware, in north-west London, two weeks ago.
The amnesty, a joint operation between the Government and the Association of Chief Police Officers, will run until the end of June. People will be asked to hand over knives and other sharp weapons to police without fear of prosecution.
But a Home Office spokesman admitted this week that the campaign is unlikely to work in isolation. "Ministers see the amnesty as one of many tactics to halt the number of knife crimes, including those in schools," he said. "It must work alongside other police initiatives to raise awareness of the dangers of carrying knives and other weapons.
"It would be wrong to have knee-jerk reactions, and there are a number of measures in place already that should make schools safer."
He praised the work in schools by West Midlands police, the force that is investigating the latest school stabbing. It has produced a DVD, called "Tooled Up for School", which is used in citizenship lessons. It includes rap music, fictional drama and interviews with the families of victims, including the parents of Luke Walmsley, who was stabbed at Birkbeck secondary in North Somercotes, Lincolnshire, in 2003. The DVD is part of a campaign called oneknifeonelife.
Last November, the then Home Office minister Hazel Blears announced that the Violent Crime Reduction Bill contained measures that would allow teachers to confiscate pencil sharpeners, scissors and other sharp objects from pupils.
A spokesman said: "That Bill will allow teachers not just to search desks and pencil cases, but pupils. Teachers, as well as pupils, have a right to feel safe in schools."
NASUWT, the second-largest teaching union, is calling for airport-style walk-through security scanners to be introduced in schools. But Chris Keates, the union's general secretary, said that stabbings in schools remain very rare.