The United States said Wednesday it agreed with China to hold a virtual meeting between U.S. President Joe Biden and Chinese leader Xi Jinping by the end of the year, as Washington seeks to manage the growing rivalry between the nations.

The announcement was made following talks between U.S. National Security Adviser Jake Sullivan and China's top diplomat Yang Jiechi in Switzerland, which, according to a senior Biden administration official, lasted for six hours and touched on U.S. concerns over China's possible human rights abuses as well as its pressure on Taiwan.

Combined photo shows U.S. National Security Adviser Jake Sullivan (L) and China's top diplomat Yang Jiechi. (Kyodo)

"We do have out of today's conversation an agreement in principle to hold a virtual bilateral meeting between the leaders before the end of the year," the official said, speaking on condition of anonymity.

Sullivan suggested in June that Biden and Xi could meet on the sidelines of a Group of 20 summit to be held in Italy at the end of this month. But Xi has not left China during the coronavirus pandemic and has no plans to travel to Italy.

White House Press Secretary Jen Psaki said the two countries are working out the details of the meeting, with the Biden administration believing that leader-level engagement is "an important part of our effort to responsibly manage the competition with China, especially given the coalescing of power in Chinese leadership."

During their talks in Zurich, Sullivan raised "a number of areas" of U.S. concern such as Beijing's alleged human rights abuses against the Muslim Uyghur minority in its far-western Xinjiang region, the crackdown on Hong Kong democracy, and the situations in the South China Sea and Taiwan, where China has been increasingly assertive, according to the White House.

He also made clear the United States will oppose any unilateral actions to change the status quo on Taiwan, the senior Biden administration official said.

But the U.S. national security adviser also pointed out areas where the two countries can work together, possibly including efforts to address climate change, and discussed ways to manage risks in the bilateral relationship.

Yang, for his part, told Sullivan China opposes defining China-U.S. relations as "competitive," and that confrontation would cause serious damage to both countries and to the world, according to China's official Xinhua News Agency.

He also demanded the United States respect China's sovereignty, security and development interests, and not interfere in China's "internal affairs," referring to issues such as Taiwan, Hong Kong and Xinjiang.

Yang is a member of the Political Bureau of the Chinese Communist Party's Central Committee.

The high-level meeting followed a phone conversation in early September between Biden and Xi, during which they discussed the need to ensure competition does not descend into conflict. It was their second phone call since Biden took office in January.

 Then U.S. Vice President Joe Biden (L) is escorted by his Chinese counterpart Xi Jinping during a welcoming ceremony at the Great Hall of the People in Beijing on Aug. 18, 2011. (Kyodo)

For Sullivan, it was his first in-person meeting with Yang since March, when they met in Alaska with other top diplomats from the two countries and engaged in rare public sparring over their differing visions for the international order and their respective positions on human rights and democracy issues, among other topics.

Wednesday's meeting had a "different tone than Anchorage" and the conversation was "candid" and "wide-ranging," according to the senior Biden administration official.

Xinhua reported that the two sides had "a comprehensive and in-depth exchange of views" on China-U.S. relations as well as international and regional issues of common concern. It also said the meeting was described as "constructive and conducive to enhancing mutual understanding."

The Zurich meeting took place as tensions are growing over China's increased military pressure on Taiwan, a self-ruled democratic island Beijing considers a renegade province awaiting reunification, by force if necessary.

On Monday, 56 Chinese military planes entered Taiwan's air defense identification zone, a one-day record since Taipei began disclosing such figures in September last year, leading the White House to express concerns over the provocative action.

China's move may also have been a reaction to military exercises involving three U.S. and British aircraft carriers, Japan Maritime Self-Defense Force destroyers and other countries' naval forces in waters southwest of Okinawa.

Taiwan and mainland China have been separately governed since they split as a result of a civil war in 1949.

The United States switched its diplomatic recognition from Taipei to Beijing in 1979. But Washington maintains substantive, though unofficial, relations with Taiwan and supplies the island with arms and spare parts to maintain sufficient self-defense capabilities.

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