Ban spoke in Malaysia a day after the 15-nation council adopted a statement demanding that Syria "immediately" implement a peace plan proposed by UN-Arab League envoy Kofi Annan and gave a veiled warning of international action.
"As the situation on the ground continues to deteriorate, it is more urgent than ever to find a solution," the United Nations secretary-general said in a speech in Kuala Lumpur.
"I hope that this strong and united action by the council will mark a turning point in the international community's response to the crisis," Ban said, echoing comments made by his spokesman after the statement was adopted.
The UN says well over 8,000 people have been killed in Syria in the past year as President Bashar al-Assad's government has sought to crush a popular revolt.
Following intense negotiations among the major UN powers, Russia and China signed up to the Western-drafted text which calls on Assad to work toward a cessation of hostilities and a democratic transition.
Russia and China have vetoed two Security Council resolutions on Syria that were backed by the United States and Europe, saying they were unbalanced.
The statement, which carries less weight than a formal resolution, gives strong backing to a six-point plan that Annan, the former UN secretary-general, put to Assad during talks in Damascus this month.
Ban said the statement called for an immediate end to violence and human rights violations "in clear and unmistakable terms".
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I wonder how many Syrian's have been slaughtered before China and Russia were finally embarrassed enough to say "enough". Shame on Assad - shame on China and Russia.