In Australia, Mr. Xi and the Australian prime minister, Tony Abbott, declared the completion of a China-Australia free-trade pact, 10 years in the making, that will open China’s markets to Australian beef, dairy products and that Tasmanian salmon.

“The last two weeks showed that in Asia, even though China is not a security partner, China is an important economic partner,” said Wu Xinbo, director of American studies at the Institute of International Studies at Fudan University. “It shows the United States can say a lot about regional prosperity but doesn’t do much. China only says some things, but does a lot.”

What Mr. Xi did say in Australia, though, was intended as reassurance backed by resolve.

In an address to Parliament, he spoke of China’s power relative to its regional neighbors. “China is a large country of over 1.3 billion people,” he said. “It is like the big guy in the crowd. Others naturally wonder how the big guy will move and act, and they may be concerned that the big guy may push them around, stand in their way or even take up their place.”

China, he said, is interested in delivering development to the Asia-Pacific region through its own prosperity in “a virtuous cycle of development and security.”

Beneath the reassurance, though, was a sharp message, reminding Australia that China would stand firm in upholding the “core interests” of its sovereignty and territorial integrity.

Looking at the longer term, Mr. Xi seemed to be trying to entice Australia, one of America’s closest intelligence-sharing allies, away from its more than half-century alliance with Washington. “We have every reason to go beyond a commercial partnership to become strategic partners who have a shared vision and pursue common goals,” Mr. Xi said.

Hugh White, professor of strategic studies at the Australian National University, said: “Xi and his colleagues are very serious about their strategic ambitions. In the long run they believe that the gravitational force of China’s economy will pull Australia into its political and strategic orbit and keep it there.”