The appeal came in a report by the secretary general to the Security Council that also made the case for stepped-up efforts to reach a political solution and end the nearly four-year war.
"This conflict has become business as usual," Ban wrote in the report, obtained by AFP.
The UN chief listed five priorities for action including the lifting of sieges on 212,000 people, ensuring access to medical aid to all of Syria and rebuilding the education system.
The report was the 12th to the council, which has been deeply divided over the war that has left more than 210,000 dead and displaced 12 million Syrians.
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Russia, President Bashar al-Assad's ally, has blocked moves to punish the regime for the worsening violence.
Ban reported a significant escalation of violence and attacks by government forces during January in Damascus, rural Damascus and in eastern Ghouta.
Assad's forces conducted aerial bombardments including with barrel bombs, shelled the area of eastern Ghouta and launched surface-to-surface missiles, the report said.
"I haven't heard of (the) army using barrels, or maybe cooking pots," Assad said, laughing.
"We have bombs, missiles and bullets," he added, dismissing claims his forces were using indiscriminate weapons.
Ban said barrel bombs were used against civilians in Aleppo, where the United Nations is seeking to freeze fighting as part of peace efforts.
Assad's forces are besieging 185,500 people in eastern Ghouta, Darayya and Yarmouk while armed opposition groups in Nabul and Zahraa are preventing 26,500 people from gaining access to food and other supplies, the report said.