"Children are increasingly bearing the brunt of this conflict," the London-based organisation says in a report published on Monday.
"Both the Israeli Defence Force and Palestinian armed groups show an utter disregard for the lives of children and other civilians," it adds.
The report says more than 250 Palestinians under 18 years of age, and over 70 young Israelis have been killed during the two-year Palestinian uprising.
In the latest incidentd on Monday, a teenage Palestinian boy was killed by machine-gun fire in the West Bank city of Nablus as Israeli tanks moved into a refugee camp.
A second boy and an Israeli soldier were killed in a fight between Israeli forces and Palestinian gunmen that raged on after nightfall in central Nablus.
Moments of horror
The report comes just before the second anniversary of the death of Muhammad al-Durrah - the 12-year-old boy who was killed in a hail of bullets beside his father.
He was the first child to die in the intifada. His final moments were captured on television and provoked outrage around the world.
The report cites four cases which embody the fate of children caught up in the conflict:
Crime, but no punishment
The report urges both sides to act against those responsible.
It says the Israeli army did not punish soldiers who responded to stone-throwing children with "unlawful and excessive use of lethal force" at demonstrations.
Palestinian leaders have also failed to rein in suicide bombers who deliberately target children and other civilians, the report says.
"Both the Israeli government and the Palestinian Authority must act swiftly and firmly to investigate the killing of each and every child and ensure that all those responsible... are brought to justice," Amnesty said.
It also called for international observers in the region, saying their presence might "have saved the lives of Israeli and Palestinian children as well as other civilians".
Israel rejects the need for international observers.
Palestinian cabinet minister Saeb Erekat told Reuters news agency that he blamed the "tragic death of Palestinian and Israeli children on the Israeli occupation, which is evil in itself".
Israeli officials said it was wrong to compare their army, using force to quell demonstrations, with bombers who deliberately target civilians.
"We are defending ourselves and it is unavoidable that people get killed in self-defence," cabinet minister Yitzhak Levy told Israeli television.