The two sides held firm to their stances on a hot-button issue which has added to broader tensions between the rival superpowers, but US officials said it did not undermine Mattis's effort to rescue the fraying relationship between the two militaries.

Mattis's talks with Xi, his Chinese counterpart Wei Fenghe, and politburo member Yang Jiechi found general agreement on North Korea, Afghanistan, and some other lesser issues, successfully planting the seeds for better cooperation and dialogue, including a possible visit by Wei to the Pentagon, the officials said.

Both sides avoided digging into the ongoing trade tensions, focusing instead on smaller areas where security forces might build a rapport over time, helping to avoid conflict.

Demonstrating their willingness to engage, the Chinese turned out a marching band playing the US and Chinese national anthems, and paraded troops for Mattis to review, in addition to giving the US defense chief time with the Chinese president.

"The Chinese-US relationship is one of the most important bilateral relationships in the world," Xi said. "The common ground of the two parties far exceeds the differences."

Overall, "the discussions were candid and positive," said Pentagon spokeswoman Dana White.

"Areas of disagreement were identified but not necessarily dwelled on."

- Chinese territorial claims -

Mattis came to China amid an escalating war of words over the South China Sea, rising Chinese pressure on US ally Taiwan, and China's long-term ambition to challenge US power across the Indo-Pacific region.

After Beijing installed missile batteries and landed long-range bombers on some of the reclaimed South China Sea outposts, Mattis publicly accused Xi of reneging on his pledge against militarising the region, and the Pentagon disinvited Chinese forces from participating in a Pacific Rim exercise.

Going into the visit, though, Mattis toned down his comments, saying he mainly wanted to take the pulse of China's military strategy and intentions, and find areas where they could work together and build trust.

China meanwhile has accused the United States of tightening its ties with Taiwan, which Beijing regards as an outlaw province, and the issue was raised multiple times in Wednesday's talks.

In a statement after his meeting with Mattis, Xi stressed that China would not back down on its claim to the islands.

"While seeing the existing common interests of China and the United States, we also do not shun the differences that exist between the two sides," Xi said.

"Regarding the issue of China's sovereignty and territorial integrity, our attitude is firm and clear. From the territory left by our ancestors, (we will not) give up even one inch."

US Assistant Secretary of Defense Randy Schriver, an Asia expert who joined Mattis in the talks, said the two sides agreed to continue the discussion on the South China Sea, and not let it overtake the visit's main mission, of finding where the two militaries could work together.

Schriver said China reaffirmed its support for the US effort to push North Korea to give up its nuclear weapons, and the UN Security Council resolution placing heavy sanctions on North Korea.

China also offered support for US efforts to foster talks in Afghanistan between the government and the Taliban, and explored more cooperation at a lower level, on issues like counterterrorism and fighting piracy.

Throughout the talks, said Pentagon spokeswoman White, there was a "pretty consistent theme" that the Chinese want to build a durable military-to-military relationship, as a stabilising factor in the overall bilateral relationship.

"Since ancient times, to know the art of war is not to like doing war," Xi said.

"Strengthening exchanges and mechanisms at all levels between the two armed forces will help to dissipate misgivings and to prevent misunderstandings, miscalculations and accidents," Xi said.

Mattis will continue meeting Chinese officials through Thursday morning, and then fly to Seoul and Tokyo. He will reaffirm the US security commitment to its East Asian allies amid some nervousness about Trump's embrace of North Korean leader Kim Jong Un.