UN-Arab League envoy Lakhdar Brahimi warned alongside Ban that Syria is now in danger of becoming a "failed state" as he appealed for new international efforts to reach a political settlement.
The UN estimates there are currently more than 460,000 refugees in countries around Syria and in North Africa with another 20,000 in Europe, Ban told a UN General Assembly meeting on conflict.
"We expect the total number of refugees to reach 700,000 by early next year," he said, adding that he would soon visit refugee camps in Jordan and Turkey.
"The conflict in Syria, now in its 21st month, is reaching new and appalling heights of brutality and violence," Ban said, highlighting how President Bashar al-Assad's government and the opposition have both stepped up attacks.
Stressing that the UN could not confirm the figures, Ban highlighted reports that up to 40,000 people have been killed since March last year.
Brahimi told the same meeting that unless moves are made toward a political settlement, Syria would become "a failed state with all the predictable dire consequences for the people of Syria, for the entire region and for international peace and security."
He warned that the crisis could see "the state and its institutions withering away, lawlessness spreading, warlordism, banditry, narcotics, arms smuggling and worst of all the ugly face of communal and sectarian strife take hold of Syria."
Voice of Russia, AFP