The United States and China must work to ensure that talks between their leaders at a G20 summit this month go well and they manage differences, a top Chinese diplomat said, as the two countries try tentatively to get ties back on track.
"We made clear that the United States will continue to fly, sail and operate wherever global law allows", Mattis said.
Despite the airing of grievances, the talks appeared aimed at controlling the damage to relations that has worsened in recent months and at paving the way for an encounter between U.S. President Donald Trump and Chinese President Xi Jinping at the Group of 20 summit in Argentina at the end of November. China expects the U.S. "to respect China's security interests in the Asia-Pacific, China's sovereignty and development interests", Yang said Friday.
"The United States is not pursuing a Cold War or containment policy with China", Pompeo told a joint news conference.
During Friday's dialogue, USA officials also reaffirmed "strong ties" with Taiwan, which has been self-ruled since the 1940s but claimed by China. "Rather, we want to make sure China acts responsibly and fairly".
Secretary of State Mike Pompeo, Defense Secretary Jim Mattis, Chinese politburo member Yang Jiechi and Defense Minister Wei Fenghe will take part in the talks.
However, Yang and Chinese defense minister Wei Fenghe spoke of the need to improve cooperation, including between the USA and Chinese militaries, to ease the risk of conflict as the two powers jockey for pre-eminence in the Asia-Pacific.
China's President Xi Jinping (L) and US President Donald Trump attend a welcome ceremony at the Great Hall of the People in Beijing on 9 November 2017.
"We have continued concerns about China's activities and militarization in the South China Sea", Pompeo said following the talks.
Defense Secretary Jim Mattis asserted US rights to freedom of navigation but also said the two sides should work together on areas of common interest.
Mattis did meet Wei in Singapore on 18 October and told him that the world's two largest economies needed to deepen high-level ties to reduce the risk of conflict. "And let's not forget how our two sides have successfully navigated through previous rough patches in our economic and trade relations", he said.
Since then relations have soured and they have become embroiled in a major trade war in which the United States has imposed tariffs on $250 billion worth of Chinese goods and China has retaliated with tariffs on $110 billion worth of USA goods.
Mr Trump has vowed to inflict more tariffs that would hit nearly all Beijing's USA exports if China retaliates further.
Mr. Pompeo expressed concern about the building of military installations on artificial islands and reefs of the South China Sea, while Mr. Yang asserted that Beijing has sovereignty over those waters even though other countries, including some allies of Washington, reject China's claims.
Xi told former U.S. secretary of state Henry Kissinger that he and Trump would have "a deep exchange of views" in Argentina, according to the Chinese state news agency.
"The United States and the global communities will continue to express our concerns with respect to China's repression of religious groups - Christians, Buddhists, and 800,000 to possibly millions of Muslims - that have been denied their freedoms", Pompeo said during a joint press briefing following Friday's talks.
Reflecting growing USA concerns about the Chinese cyber threat, a senior US intelligence official on Thursday accused China of violating a 2015 agreement aimed at stopping cyber espionage through the hacking of government and corporate data.