"As fighting reaches the heart of heavily populated urban areas, the impact of lethal weapons will carry an even heavier toll on children."
Veneman said the war and bloodshed in Gaza would cause long-term psychological damage to children.
"The crisis in Gaza is singular in that children and their families have nowhere to escape, no refuge. The very thought of being trapped in a closed area is disturbing for adults in peace times," she said.
"What then goes through the mind of a child who is trapped in such relentless violence?"
Israel has said that it is trying to minimise civilian casualties as it targets Hamas fighters and their infrastructure, but Palestinian children are being subjected to harrowing experiences.
"I saw the soldier standing next to the shop. I looked for my mum and then he shot me. One bullet him my hand and the other went through my back and out through my stomach," Samar, a young girl, told Al Jazeera while recovering from her wounds at a Gaza hospital.
Amal, another young girl, wailed: "We have nothing to do with this, we don't fire rockets, we don't know what this war is about."
More than 40,000 pregnant women and their unborn children were also believed to be at risk because Gaza's overwhelmed hospitals were unable to take them in.
Dr Walid Sarhan, a Jordanian psychiatrist, said that if nothing is done to help traumatised children Gaza would begin to see advanced cases of psychiatric problems.
"The main one would be post-traumatic stress disorder, which is expected to rise 60 or 70 per cent among children," he said.
"Also they will have behavioural and emotional problems. They will have difficulties returning to school, going on to achieve in school, and this will not be in small numbers."
Mark Regev, an Israeli government spokesman, said that thousands of children in southern Israel were also suffering because of Palestinian rocket fire.
"Two weeks before this crisis started I went down south with my prime minister, Mr Olmert ... and he was given letters from fourth graders I believe, children who are nine and 10-years-old, who their entire lives have been on the incoming end of these Hamas rockets," he told Al Jazeera.
"You have a whole generation of Israeli children who unfortunately suffering similar trauma."