As he began a nine-day trip to the Asia-Pacific region Friday, President Obama was aiming to reassure jittery U.S. allies and emerging nations that they have another avenue to prosperity at a time when an increasingly aggressive China is extending its sphere of influence.

At each stop — a pair of regional summits in Hono­lulu and in Bali, Indonesia, bookending a visit to Australia to highlight a military alliance — Obama is expected to send a clear signal that the United States is a “Pacific power,” eager to help build economic success and security in the fast-developing region.

In doing so, the president will make it clear the Chinese must “follow the rules of the road,” as one administration official put it this week.

High on the list of U.S. priorities is getting commitments from China to enact more flexible currency rate standards to help balance trade; respect intellectual property rights; and adopt a less aggressive military posture in the disputed South China Sea.

For their part, the Chinese are concerned about a budding trade pact between the United States and eight other nations, and they will be closely monitoring Obama’s visit next week to an Australian military base.

Since last year, China has fed the worries of its neighbors with a string of aggressive diplomatic and military moves, including attention-grabbing confrontations in the South China Sea, which is believed to hold valuable oil and minerals and is heavily used for commercial shipping.

The area has been in dispute for decades, with various portions claimed by Vietnam, the Philippines, Malaysia, Brunei and Taiwan. China has made the largest claim, on a U-shaped section that covers almost the entire region.

China’s increasing willingness to throw its weight around has put other countries on edge and spurred them to solicit U.S. assistance. Even Burma, also known as Myanmar, appears to be hedging against the rise of its longtime ally, releasing political prisoners in a bid to appeal to the West.

Danny Russel, senior director for Asia on the National Security Council, said that at the East Asia Summit in Bali next week, the United States and other participating nations, including China, will seek consensus on “international norms and law — freedom of navigation, the right to unimpeded legitimate commerce” and “collaborative efforts to avoid the accidental conflict or miscalculation . . . that could lead to a spike in tensions.”

Small signs of the U.S.-China rivalry for influence emerged even before Obama’s departure from Washington. When U.S. officials said this week that they hoped to ramp up talks on trade and green jobs growth with emerging nations at the Asia-Pacific Economic Cooperation summit in Honolulu, Beijing quickly criticized the agenda as too ambitious.

U.S. expectations are “too high” and “beyond the reach” of many developing Asian nations, Assistant Foreign Minister Wu Hailong told reporters.

Obama’s trip is part of the administration’sevolving foreign policy vision. Officials have pointed to the winding down of wars in Afghanistan and Iraq and said that now is the time to pivot toward the Asia-Pacific region.

As Wu made clear, the U.S. administration’s bolder stance has not gone over well in Beijing. Chinese officials are wary of U.S. involvement in the Trans-Pacific Partnership (TPP), a trade pact still in the works that would include at least eight other nations.

And the Chinese are keeping an eye on Obama’s visit next week to a military facility in Darwin, Australia, where he and Australian Prime Minister Julia Gillard are expected to unveil an agreement to allow U.S. Marines use of Australian bases for training and exercises.

Obama will hold a bilateral meeting with Chinese President Hu Jintao in Hono­lulu on Saturday.

In China, “there is a widespread belief that the U.S. is stirring up trouble,” said Elizabeth Economy, director of Asia studies at the Council on Foreign Relations, who is visiting Beijing this week. “The TPP is seen as something ‘mysterious’ that is designed in some way to contain China. . . . The dominant theme I am hearing here is that the international community is always asking for more from China and not appreciating what China already contributes to the global system.”

Indeed, a growing number of nations, including Australia, count China as their largest trading partner, critical to their economies. The Obama administration is eyeing China's vast consumer base as a huge opportunity for U.S.-produced goods. In Southeast Asia, China has ramped up its aid to emerging economies.

With its economic growth, however, has come increased aggression, bolstered by the rapid modernization of its military. Defense spending has seen double-digit growth in China for much of the past two decades.

This year, China launched its first aircraft carrier — a retrofitted Soviet vessel. It is developing an anti-ship missile that could limit the range and options of U.S. aircraft carriers should a conflict arise over Taiwan. And earlier this year, just hours before a visit by then-defense secretary Robert M. Gates, China debuted its new J-20 stealth fighter in a provocative test flight.

In a tour of Asia last month, Defense Secretary Leon E. Panetta told two of America’s closest Asian allies — Japan and South Korea — that the United States is committed to the region. Even in the face of defense budget cuts, he vowed, “we are not anticipating any cutbacks in this region. If anything, we’re going to strengthen our presence in the Pacific.”

Douglas Paal, head of the Asia program at the Carnegie Endowment for International Peace, said Obama must reassure allies that the United States will be more focused on Asia than it has been for the past decade.

“The U.S. has no ability to keep China out or to keep China down,” Paal said. But at the same time, he added, the United States has too many interests in the Asia to be absent.

“We haven’t been tending [those interests] properly since 1997,” Paal said. “And now you have to do the hard work to get back in after exempting yourself for 12 years.”