WASHINGTON — After a rocky year for U.S.-Chinese relations, Defense Secretary Robert Gates heads to China in hopes of strengthening relations with the rising military power and global competitor.

The relationship between the two countries has been strained recently as China expanded its firepower and reach, quarreled with U.S. allies over Pacific territory and broke off the few flimsy military ties it had allowed with Washington.

Gates, who flew to Asia on Saturday, will meet with Chinese President Hu Jintao a week ahead of Hu’s planned state visit to Washington.

In talks with Hu and Chinese military leaders, Gates plans to make the case for regular face-to-face discussions between military officials from both countries. Direct discussions are already routine for presidents and diplomats.

Limited relations between the two militaries were restored late last year. On the eve of Gates’ trip, an aide said Gates saw the military relationship on the mend.

"He goes into it encouraged, optimistic, hopeful," Pentagon press secretary Geoff Morrell said Friday, noting that Gates will tour a major Chinese nuclear facility and meet with uniformed leaders.

Still, there are few signs that China wants the kind of broad engagement Gates has argued would help avert risky misunderstandings and miscalculations as China extends its military reach.

"We’ve raised a lot of these issues before. We’ve raised them in Beijing, we’ve raised them in Washington," Morrell said. "We will raise them again and we certainly hope we make additional progress and sustainable progress."

The United States and China are sometimes global competitors for markets, influence and increasingly for military bragging rights.

But they also are diplomatic partners, and Gates’ visit comes as the Obama administration is leaning hard on China to tighten the leash on its erratic ally North Korea, which in recent months has come close to open conflict with South Korea. Gates is also visiting South Korea, for brief talks about averting war with the North, as well as Japan, which is alarmed by Chinese military moves.

The China invitation is a coup for Gates, who invited a Chinese counterpart for similar talks and a visit to the U.S. nuclear weapons headquarters in 2009. A reciprocal invitation was expected in 2010, but China withheld it in protest of a planned $6.4 billion arms sale to China’s rival, Taiwan.

The U.S. and China have cooperated on penalties against Iran over its nuclear program, and both nations are discussing working side by side to deter piracy and respond to Asian natural disasters.

But the two militaries are engaged in a test of wills in the Pacific, as China begins to challenge the century-old assumption that the United States is the pre-eminent military power there.

China has made significant gains toward fielding a missile system designed to sink a moving aircraft carrier from nearly 2,000 miles away, the top U.S. commander in the Pacific said Thursday. The so-called carrier-killer missile and a new showpiece stealth fighter jet may not be a match for U.S. systems but represent rapid advances for China’s homegrown technology and defense manufacturing.