By Kristin Roberts

WASHINGTON, Feb 28 (Reuters) - U.S. Defense Secretary Robert Gates' visit to Asia this week was aimed at deepening strategic ties with regional leaders and showing that Washington remained engaged, but China's explosive rise was never far from the surface.

Gates visited three large democracies -- Australia, Indonesia and India - all U.S. allies, and offered to help each build its military might.

He discussed joint missile defense systems in Australia and India and military aircraft orders in all three countries.

In Jakarta, he offered to help train the Indonesian military and update its fleet of military transport aircraft, and in India he encouraged officials to choose U.S. fighter jets when it orders combat aircraft this year.

"I think we moved them all forward," Gates said on the return flight to Washington.

At every meeting, government officials raised with Gates the issue of China's growing role and influence, according to one senior U.S. defense official traveling with the Pentagon chief.

And while Gates publicly dismissed the idea that the Pentagon was trying counterbalance Beijing, his aides suggested otherwise.

In India, for example, another U.S. official said New Delhi is seeking the type of modern naval and air power that can be projected great distances.

"As India is looking to its future it aspires to be not just a regional power but a global power," the official said. "Looking around the world they saw that they are falling behind, they need to modernize."

Some of the military modernization programs discussed at the meetings and the possibility of missile defense cooperation with the United States could complicate the countries' relations with China, ties in large part built on significant economic links.

GREAT POWER

Relations between China and the United States have improved since 2001, when the countries' militaries broke contact following a collision between a Chinese fighter jet and U.S. spy plane.

But many differences remain between Beijing and Washington over China's military buildup, U.S. weapon sales to Taiwan and over international issues.

Military relations were strained again late last year when China denied a U.S. Navy aircraft carrier group and two smaller ships access to the Hong Kong port. Those events and others have led U.S. officials to charge China with failing to live up to its obligations as a "responsible" power.

"China obviously has become an economic powerhouse and with that economic role in the world has come an increase in political influence as well," Gates told reporters during the trip. "China is a great power."

But he stressed the Pentagon was not reaching out to any nation as a response to Beijing's activities.

"I don't see our improving military relationships in the region in the context of any other country, including China," he said. "These expanding relationships don't necessarily have to be directed against anybody."

Instead, Gates, who was nursing a broken arm during the trip, said his goal was to let those countries know the United States was still engaged despite big commitments in Iraq and Afghanistan.

One senior U.S. official said Gates had been shocked by the Pentagon's neglect of some countries, noting it had been years since a U.S. defense secretary visited.

"To put it plainly, I think they were surprised that I went ahead with the trip having broken my arm," Gates said en route to Washington. "I think the fact that I felt it was important enough to stick with the trip and visit these places maybe had some impact as well."

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