UN agencies helping to care for the millions driven from their homes in Syria by two years of conflict warned on Tuesday that they face "impossible" choices as funding fails to meet soaring needs.

"Agencies including UN and NGOs are forced into the impossible situation of having to prioritise equally compelling programmes," Lebanon representative for the UN High Commissioner for Refugees (UNHCR) Ninette Kelley said in a statement.

"At this level of funding, vital programmes to ensure food, clean water, schooling for children, health care and shelter for newly arrived refugees are simply impossible."

Neighbouring Lebanon has taken in more than 400,000 Syrian refugees since the conflict erupted in March 2011, equivalent to some 10 percent of the country's population. More than 3,000 more refugees are registered each week.

An appeal for funding by aid organisations working with the refugees secured just a third of the money sought.

"In one month, and with the current funding, more than 400,000 Syrian refugees in Lebanon will no longer receive food assistance" said Etienne Labande of the World Food Programme.

"I am extremely concerned that without continued funding we will see increased tensions and further displacement in an already tense environment."

The UN children's fund warned that as well as housing and health care, the continued provision of schooling for the many children among the refugees was also at risk.

"The children affected by this crisis -- making up more than half of the refugee population -- are facing challenges that risk lasting, disastrous impact on their lives," UNICEF official Annamaria Laurini warned.

"If significant additional funding is not received soon, UNICEF will be unable to respond to exponentially growing needs of these most vulnerable victims of this human tragedy."

UNHCR regional aid coordinator Panos Moumtzis warned on Tuesday that aid operations for Syrian refugees were at "breaking point".

"We want to ring the alarm bell. We are at a breaking point," Moumtzis said in a statement released in Geneva.

In all, some 1.3 million people have now fled Syria and some 200,000 more are crossing into neighbouring countries each month.