U.S. Deputy Defense Secretary Ashton Carter wanted to convey a message to allies, security partners — and potential adversaries — in the region that despite big budget cuts and political infighting in Washington, the United States will remain a resident Pacific power committed to helping maintain the peace that supports economic growth.

The most immediate challenge to regional stability comes from North Korea, which conducted a third nuclear test on Feb. 12 in defiance of United Nations Security Council resolutions. Pyongyang said that the underground test was designed to perfect small nuclear warheads for ballistic missiles to strike the U.S. mainland or American bases in Japan and other parts of Asia.

While Carter was in the region, Pentagon officials disclosed that B-52 bombers, based on the U.S. territory of Guam in the western Pacific, flew a training mission over South Korea on March 8 and would continue to do so as a symbol of American resolve and deterrent power.

However, the U.S. and many countries in East Asia worry that another looming challenge to regional security may come from China. They are concerned that China might use its growing economic and military strength to become a domineering force in regional affairs.

Carter’s tour, which ended in Jakarta on March 20, followed a speech to the Asia Society in New York earlier in the month by U.S. President Barack Obama’s National Security Advisor Thomas Donilon. He said that America’s future “has never been more closely linked to the economic, strategic and political order emerging in the Asia-Pacific.”

Asia, one of the fastest growing economic zones in the world, already accounts for more than 25 percent of global GDP. In the next five years, nearly half of all growth outside the U.S. is expected to come from Asia. America wants to plug into that trade, investment and business dynamism and remain part of it for the long term.

Donilon said that the Obama administration had not only made the strategic decision to allocate more diplomatic, economic and military resources to the Asia-Pacific area, but also to rebalance within Asia to recognize the growing importance of Southeast Asia.

But is the U.S. rebalance sustainable? This is the question that most concerns Japan and other Asia-Pacific nations which want America fully engaged in the region to help keep the peace and discourage China from using force or intimidation to achieve its objectives.

If economic strength is the currency of power in the 21st century, the most critical factor in continuing U.S. engagement and influence in the region will be whether its economy revives and prospers. The jury is still out on that question. Meanwhile China, the world’s second biggest economy after the U.S., has used the attraction of its huge market to become the top trading partner of almost every East Asian economy.

On the military front, Carter said in Seoul that with U.S. forces out of Iraq and soon to leave Afghanistan, the Pentagon could shift a great amount of military weight to the Asia-Pacific. He described the U.S. focus on the region as an “historic priority,” adding that “we have the resources to accomplish it and no matter what happens in the budget debates our commitment to the Asia-Pacific rebalance … will remain firm.”

He is probably right. Although U.S. defense spending faces sharp curbs, it does so from a very high level. The U.S. military budget is still many times greater than China’s. In fact, it equals the official military outlays of China and the next 13 biggest military powers combined.

Still, the gap in military spending between China and the U.S. is closing fast. China capped a series of double digit increases in annual military spending over the past two decades when it announced a 10.7 percent rise in its defense budget on March 5. It now spends more on its armed forces than neighboring Japan, South Korea and Taiwan combined.

The International Institute for Strategic Studies (IISS) reckons that if the 15 percent average annual increases in China’s official defense budget in the past decade continue over the medium term, Chinese military outlays could rival U.S. base defense budget spending by 2025. The base defense budget does not include the costs of wars.

If additional parts of military spending widely believed to be excluded from the official budget of the Chinese armed forces are added to the equation, convergence could occur in 2023, just 10 years away, according to the IISS.

Yet it is easy to see how the U.S. appears threatening to China when it spent six times as much on defense in 2012 and has formal alliances or strategic partnerships with Japan, India and South Korea, respectively the third, fourth and fifth strongest military powers in Asia.

Reconciling these differing threat perceptions — and the divergent interests that underlie them — will be a major test of statesmanship for the Obama administration and the new Chinese leadership that has taken the reins of power for the next 10 years.