"The engines of growth and economic power continue to shift with the rise of the Asia-Pacific region as a centre of dynamism and influence," Ban said.
"I welcome the growing global prominence and engagement of China and India, key Member States and close partners of the United Nations on many of the Organization's priority areas," he said in his address to Stanford University.
Ban was in San Francisco yesterday to commemorate the 70th anniversary of the adoption of the UN Charter.
"I look forward to seeing regional economic integration, including free movement of goods, services, investment, skilled labour and a freer flow of capital," he said.
He said Asia also faces challenges that could put at risk global goals of prosperity, stability and dignity for all.
These include competing territorial or maritime claims, political and communal tensions, and non-traditional security threats such as transnational organised crime and terrorism, he added.
He also stressed that he has consistently called on all parties to resolve their disputes in the South China Sea in a peaceful and amicable manner, through dialogue and in conformity with international law, including the UN Charter.
On the migration crisis in Southeast Asia, Ban said people in search of asylum are being left trapped at sea and saving lives must be the number one priority.
"Resolving this complex situation also requires addressing the root causes of migration, which include human rights violations and lack of economic opportunities," he said.
On the Rohingya Muslim community in Myanmar, Ban said three years after the inter-communal violence in western Rakhine state, some 130,000 still remain in camps requiring urgent humanitarian assistance.
He voiced regret that relations between North and South Korea remain at a low ebb, saying that improved relations would benefit both nations and the region as a whole.
"That is why I offered to visit the Kaesong Industrial Complex," but North Korea cancelled that trip, he said.
