Obama stressed spending cuts in the United States would not affect the Asia-Pacific, saying the U.S. is "here to stay."
His comments are seen as a challenge to China, which strives to be the leading power in the region.
Obama announced a plan Wednesday to station a U.S. Navy task force in Australia in 2016.
The measure will eventually see 2500 U.S. soldiers based in the North.
Define the region
The Chinese authorities have so far remained silent on the issue, with a spokesman for the Foreign Ministry suggested that the installation of U.S. Marines was not compatible with the goal of achieving an increase of peace in the continent .
China is locked in a territorial dispute with allies of the United States, including the Philippines and Taiwan, over island groups in the South China Sea.
Beijing has repeatedly insisted that he would discuss the issue only with the countries directly involved, which excludes U.S. involvement.
But analysts believe that increased presence of the United States in the region is bound to embolden his allies and irritate Beijing.
Speaking in Canberra, Obama said the Asia-Pacific countries would play a key role in shaping the world in the 21st century.
"With most of the world nuclear powers and some half of humanity, Asia will largely determine whether the next century will be marked by conflict or cooperation, unnecessary suffering or the progress of humanity" , he said.
The United States has been slow to recover from a recession, and the army is a domain of significant spending cuts.
With U.S. troops leave Iraq and Afghanistan after the long commitments, there was speculation that the Americans could also seek to play a discreet role in all of Asia.
But Obama said: "As we end the wars of today, I directed my national security team to make our presence and mission in the Asia-Pacific region a top priority.
"As a result, reductions in U.S. defense spending will not - I repeat, will not - at the expense of the Asia-Pacific."
It committed the U.S. to play a "more important and long-term development of the region," adding that he was willing to work with China.
"We have seen that China can be a partner, to reduce tensions on the Korean peninsula to the prevention of proliferation," he said.
"We will seek more opportunities for cooperation with Beijing, including increased communication between our members, to promote understanding and avoid a miscalculation."
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