The UN chief said in a statement on Friday that he is "deeply concerned by the desperation shown by the people fleeing in a massive exodus from Eastern Ghouta and Afrin", Xinhua news agency reported.
Eastern Ghouta has grabbed headlines recently amid a government resolve to recapture that sprawling area while at the same time allowing civilians to leave as around 400,000 people still live in that rebel-held enclave.
"I urge all parties to the conflict to fully respect international humanitarian and human rights law and guarantee the protection of civilians," he said, noting that "any evacuation of civilians must be safe, voluntary, and in strict accordance with protection standards under international humanitarian and human rights law."
"It is also imperative that all those displaced are allowed to return voluntarily, in safety and in dignity, to their homes as soon as the situation allows it. I call on the Security Council to stand united and take concrete steps to urgently end this tragedy," he added.
The United Nations and its partners are fully mobilised to bring immediate life-saving relief to all those in need, the secretary-general said. "I call on all parties to ensure safe and unimpeded humanitarian access in all areas."
"The reality on the ground across Syria demands swift action to protect civilians, alleviate suffering, prevent further instability, address the root causes of the conflict and forge, at long last, a durable political solution in line with resolution 2254," said the UN chief.
Thousands of civilians were fleeing from besieged enclaves on Friday as two major battles in the multi-sided war entered decisive phases, with hundreds of thousands of people trapped in the path of both assaults.
The UN Security Council on February 24 unanimously adopted resolution 2401 demanding a cease-fire of at least 30 days across Syria that would allow humanitarian access and urgent medical evacuations.