He also said India and US will continue to expand their military exercises and maritime cooperation so that the two forces become "interoperable".
Obama said during his visit to India last year, Prime Minister Narendra Modi and he agreed to a new joint vision for the Asia Pacific and Indian Ocean region.
The Asia Pacific region has witnessed tension after China flexed its military muscle in the resource-rich South China Sea.
The South China Sea is also a major shipping lane. Over half of the world's commercial shipping passes through the Indo-Pacific waterways.
China claims almost the whole of the South China Sea, resulting in overlapping claims with several other Asian nations like Vietnam and the Philippines, Malaysia and Brunei.
The US has criticised Beijing for building artificial islands in the disputed sea, and has flown a B-52 bomber and sailed a guided-missile destroyer near some of the constructions China has made in recent months.
"Our vision recognises that the Indian Ocean is vital to
the security of the region and the global economy. And it welcomes India's determination to 'Act East' with stronger security and economic partnerships across the region," the US President said.
He was replying to a question as to what role he sees for India in the emerging security situation in the Asia Pacific given what is happening and the nuclear tests by North Korea.
"It's clear that India can be an anchor of stability and security in the Asia Pacific and Indian Ocean region, and the United States looks forward to the work we can do together," Obama said.
He said "we continue to expand our military exercises and maritime cooperation so that our forces become inter operable. We are increasing our defence trade, and we're collaborating more closely to jointly develop defence technologies."
Obama said as President he has worked to renew American leadership in the Asia Pacific because the security and prosperity of the region is critical to its own and that of the world.
Obama said the US has strengthened alliances, modernised its defence posture, worked to build constructive relationship with China, helped strengthened regional institutions like ASEAN and East Asia Summit and expanded cooperation with emerging powers including India.
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