By Matt Spetalnick and Matt Siegel
BRISBANE Australia (Reuters) - President Barack Obama sought on Saturday to reassure Asia-Pacific allies about Washington's strategic shift toward the region as he sent a veiled message to a rising China with a vow to "deepen our engagement using every element of our power".
Speaking in Australia on the final stop of a three-country regional tour, Obama insisted that Asia's security order must not be based on "coercion or intimidation ... where big nations bully the small, but on alliances for mutual security".
Although Obama did not explicitly point the finger at China, there was little doubt that he was alluding to Beijing's maritime disputes with its neighbors and growing concern in the region about its military build-up.
"No one should ever question our resolve or our commitments to our allies," Obama said in a policy speech at Queensland University in Brisbane, where he is attending a G20 summit.
Obama, who visited Beijing for an Asia-Pacific summit this week and held talks with President Xi Jinping, sought to show renewed resolve for the U.S. "pivot" to the region, involving military, diplomatic and economic assets. The policy is widely seen as intended to counter China's rising influence.
But many in Asia are looking for further proof that the policy is real, with Obama's agenda dominated by crises ranging from Ukraine, Islamic State and Ebola.
"Day in, day out, steadily, deliberately, we will continue to deepen our engagement using every element of our power —diplomacy, military, economic, development," Obama said.
While reiterating the position that Washington welcomes the rise of a peaceful, stable, prosperous China, he said Beijing must prove itself to be a "responsible actor" and "adhere to the same rules as other nations, whether in trade or on the seas."
"China will inevitably play a critical role in the future of this region, and the question is what kind of role will it play?" Obama told a crowd of about 1,500 students and faculty.
Obama promised continued efforts to enhance security ties with countries as disparate as longtime close ally Japan and former foe Vietnam, both of which are locked in standoffs with Beijing over claims in the East and South China Seas. But he put forth no new security initiatives.
But even as Obama hailed the region's "dynamism," he warned of potential threats.
"We see dangers that could undermine this progress," he said, citing North Korea's nuclear and missile programs, disputes over territory that threaten to spiral into confrontation and the failure to uphold universal human rights.
His pledge to continue to stand up for human rights in the region appeared to be a nod to rights groups that have criticized the pivot for focusing on security and economics but neglecting issues like democratic freedoms.
In his speech, he singled out pro-democracy protests in Hong Kong, saying the people there were "speaking out for their universal rights" - a comment likely to irk the Chinese government. Xi made clear at his joint news conference with Obama that Hong Kong was China's affair alone.
(Editing by Raju Gopalakrishnan and Michael Perry)