U.S. Secretary of State Antony Blinken met his Chinese counterpart on Saturday in a new effort to try to rein in or at least manage rampant hostility that has come to define recent relations between Washington and Beijing. Blinken and Chinese Foreign Minister Wang Yi were holding talks in the Indonesian resort of Bali, a day after they both attended a gathering of top diplomats from the Group of 20 rich and large developing countries that failed to reach consensus over Russia's war in Ukraine and how to deal with its impacts. Wang and Blinken were discussing a range of contentious issues from tariffs and trade and human rights to Taiwan and disputes in the South China Sea. Just two days earlier, the two countries' top military officers had faced off over Taiwan during a virtual meeting. “In a relationship as complex and consequential as the one between the United States and China, there is a lot to talk about and I’m very much looking forward to a productive, constructive conversation,” Blinken said as the pair headed into the closed-door meeting. Read: USA announces new actions to support intl students' careers Wang said “it is necessary for the two countries to maintain normal exchanges” and “to work together to ensure that this relationship will continue to move forward along the right track.” He echoed frequent Chinese lines about remaining committed to the principles of “mutual respect,” “peaceful coexistence” and “win-win cooperation.” That, he said, "serves the interests of the two countries and two peoples. It is also the shared aspiration of the international community.” U.S. officials said ahead of time they don’t expect any breakthroughs from Blinken's talks with Wang. But they said they are hopeful the conversation can help keep lines of communications open and create “guardrails” to guide the world’s two largest economies as they navigate increasingly complex and potentially explosive matters. The United States and China have staked out increasingly confrontational positions, including on Ukraine, that some fear could lead to miscalculation and conflict. The U.S. has watched warily as China has refused to criticize the Russian invasion, while condemning Western sanctions against Russia and accusing the U.S. and NATO of provoking the conflict. The Biden administration had hoped that China, with its long history of opposing what it sees as interference in its own internal affairs, would take a similar position with Ukraine. But, it has not, choosing instead what U.S. officials see as a hybrid position that is damaging the international rules-based order. At the G-20 meeting, Wang made an oblique reference to China's policy on global stability, saying “to place one’s own security above the security of others and intensify military blocs will only split the international community and make oneself less secure,” according to the Chinese Foreign Ministry. On Thursday, China's joint chiefs of staff chairman Gen. Li Zuocheng upbraided his U.S. counterpart Gen. Mark Milley over Washington's support for Taiwan, which Beijing regards as a renegade province. Li demanded that the U.S. cease military “collusion” with Taiwan, saying China has “no room for compromise” on issues affecting its “core interests,” which include self-governing Taiwan, which Beijing claims as its own territory to be annexed by force if necessary. “China demands the U.S. ... cease reversing history, cease U.S.-Taiwan military collusion and avoid impacting China-U.S. ties and stability in the Taiwan Strait,” Li said. Also read: Russia and China slam NATO after alliance raises alarm At the same time, Li was also quoted in a Defense Ministry news release as saying China hoped to “further strengthen dialogue, handle risks, and promote cooperation, rather than deliberately creating confrontation, provoking incidents and becoming mutually exclusive.” China routinely flies warplanes near Taiwan to advertise its threat to attack, and the island’s Defense Ministry said Chinese air force aircraft crossed the middle line of the Taiwan Strait dividing the two sides on Friday morning. The meeting between Li and Milley followed fiery comments by Chinese Defense Minister Wei Fenghe at a regional security conference last month that was also attended by U.S. Secretary of Defense Lloyd Austin. Wei accused the United States of trying to “hijack” the support of countries in the Asia-Pacific region to turn them against Beijing, saying Washington is seeking to advance its own interests “under the guise of multilateralism.” At the same meeting in Singapore, Austin said China was causing instability with its claim to Taiwan and its increased military activity in the area. In May, Blinken incurred Chinese wrath by calling the country the “most serious long-term challenge to the international order” for the United States, with its claims to Taiwan and efforts to dominate the strategic South China Sea. The U.S. and its allies have responded with what they term “freedom of navigation” patrols in the South China Sea, prompting angry responses from Beijing.