"Syria is sliding into a large-scale humanitarian tragedy that brings back awful memories of ex-Yugoslavia," Kristalina Georgieva, the EU's international crisis chief, said in a statement.
"Civilians in Syria must be given the possibility to leave the areas of fighting in an organised and safe manner without having to fear for their life."
She released the statement the day before France takes over the presidency of the UN Security Council, after which it plans to ask for an urgent meeting on Syria - probably at ministerial level - to try to end the diplomatic deadlock and prevent further bloodshed.
French President Francois Hollande has said he will try to convince Russia and China to support further sanctions, in spite of their refusal to do so up to now.
The Syrian military is stepping up its campaign to drive rebels out of Aleppo. The opposition Syrian Observatory for Human Rights said more than 100 people, 73 of them civilians, were killed in Syria on Monday. The only international military presence is a small, unarmed UN observer mission.
The wars in the former Yugoslavia marked a failure by Europe to stop violence in its backyard. In the 1992-95 Bosnian war, around 100,000 people were killed before NATO air strikes forced the sides to the negotiating table.
"Humanitarian organisations must be granted safe access to combat zones to proceed with the evacuation of the wounded and civilians," said Georgieva, whose full title is European Commissioner for International Cooperation, Humanitarian Aid and Crisis Response.
"I appeal to the international community and in particular the United Nations Security Council to focus on the humanitarian crisis in Syria and support my call for humanitarian pauses and respect for international humanitarian law."