Syrian children walk amid tents at the Zaatari refugee camp, near the Syrian border on March 7, 2013.
UN agencies say the number of children forced to flee Syria has reached one million, describing the figure as “a shameful milestone”.
The UN’s refugee agency and Unicef say a further two million children are displaced within the country.
More than 100,000 people have been killed in the conflict, according to UN Secretary General Ban Ki-moon.
He has also called for an investigation “without delay” into the recent alleged chemical weapons attack near Damascus.
Activists say hundreds were killed in Wednesday’s attack, and Mr Ban is sending disarmament chief Angela Kane to Damascus to press for an investigation, his spokesman Eduardo del Buey said on Thursday.
‘Traumatised’
The UN says children now make up half of all refugees fleeing Syria. About three-quarters of those children are under 11.
“The youth of Syria are losing their homes, their family members and their futures,” said UN high commissioner for refugees Antonio Guterres.
“Even after they have crossed a border to safety, they are traumatised, depressed and in need of a reason for hope,” he said.
Most of the children have arrived in Lebanon, Jordan, Turkey, Iraq and Egypt, the UN says, and increasingly Syrians are fleeing to North Africa and Europe.
But with its appeal for Syria less than 40% funded, the two UN agencies say they are struggling to meet the needs of the refugees.
Just 118,000 of the refugee children have been able to continue in some sort of education, and a fifth have received psychosocial counselling.
The BBC’s Imogen Foulkes in Geneva says the agencies are now warning of a lost generation that are ill-equipped to bring peace and stability to their country in the future.
“We must all share the shame,” said Unicef executive director Anthony Lake, “because while we work to alleviate the suffering of those affected by this crisis, the global community has failed in its responsibility to this child.
“We should stop and ask ourselves how, in all conscience, we can continue to fail the children of Syria.”
The UN says the conflict in Syria has caused the world’s worst refugee crisis for 20 years, with numbers not seen since the 1994 genocide in Rwanda.
It says more than 1.7million people have registered as refugees since the uprising against the rule of Syrian President Bashar al-Assad began in March 2011.
More than 40,000 Syrians have poured over the border of Iraqi Kurdistan since a new wave of arrivals began in the region a week ago.
Shocking footage
Speaking of the alleged chemical attack, Mr Ban said: “Any use of chemical weapons anywhere, by anybody, under any circumstances, would violate international law. Such a crime against humanity should result in serious consequences for the perpetrator.”
Mr Ban has asked the Syrian government to let UN weapons inspectors, who are already in the country, investigate the allegations.
“I can think of no good reason why any party – either government or opposition forces – would decline this opportunity to get to the truth of the matter,” Mr Ban said from the South Korean capital, Seoul.
The inspection team currently only has a mandate to visit three previously agreed sites, including the northern town of Khan al-Assal, where some 26 people were killed in an alleged chemical attack in March.
But there is no sign as yet that Damascus will allow them to extend their mission.
The Syrian government has described the allegations that it sanctioned the use of chemical weapons as “illogical and fabricated”.
But unverified footage shows civilians – many of them children – apparently suffering horrific symptoms, as well as rows of shrouded bodies.
Chemical weapons experts have told the BBC that footage appears genuine and that the injuries shown are consistent with nerve agents.
International clamour over the alleged chemical attacks has continued to grow.
French Foreign Minister Laurent Fabius warned that France must react “with force” if the use of chemical weapons was confirmed.
The US state department said it was urgently gathering information to try to determine what had taken place in Damascus.