"We should stay committed to promoting peace, stability and prosperity in the Asia-Pacific region, engage in open and inclusive regional cooperation, and turn the Asia-Pacific into an important region where China and the United States work closely with each other on the basis of mutual respect," Hu said.
As to his warning on Taiwan and Tibet, Hu said such matters "concern Chinese sovereignty and territorial integrity. They touch upon the national sentiments of 1.3 billion Chinese."
It was a reference to China's claim to the currently self-governing island of Taiwan, which split from the mainland amid civil war in 1949, and to Tibet, which is already under China's control. U.S. leaders, including Obama, have irked China repeatedly by meeting with the exiled Tibetan spiritual leader, the Dalai Lama.
The U.S. and China must "treat each other with respect and as equals and handle major sensitive issues in a proper manner," Hu said.
In recent years, China has grown stronger both economically and militarily. Worrisome to the Pentagon is Beijing's increasingly aggressive stance in the western Pacific and questions over the extent to which the People's Liberation Army — which also includes China's air force and navy — is answerable to civilian leaders in the one-party government.
During Defense Secretary Robert Gates' visit to China earlier this month, the Chinese military's decision to conduct a test flight of its first aircraft designed to evade radar — the J-20 stealth fighter — appeared to catch Hu and other Chinese civilian leaders off guard. Also of concern to the U.S.: China's development of anti-ship missiles that could make it harder for American aircraft carriers to operate in the western Pacific.
Hu did not specifically mention human rights in his speech to the business leaders.
A day earlier, Hu stood alongside Obama at a White House news conference and conceded, "A lot still needs to be done in China in terms of human rights."
Those remarks were welcomed by the White House as a significant conciliatory gesture. Obama spokesman Robert Gibbs on Thursday called them a "frank admission."
"While we appreciate those words, the United States will watch the actions of the Chinese government to make sure that they meet the words that were spoken in the White House yesterday," Gibbs said.
The Chinese leader was introduced by former Secretary of State Henry Kissinger, who as national security adviser for President Richard Nixon was instrumental in 1974 in opening formal ties between the two countries.
Kissinger said normalizing U.S.-Chinese relations "after so many years of separation did shake the world."
But now, Kissinger said, "This generation has a different task. . We are working to build the world, not to shake it."
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