NEW YORK -- The U.S. and China have agreed in principle to hold a virtual meeting between Presidents Joe Biden and Xi Jinping by the end of the year.

The arrangement was confirmed at a meeting between U.S. national security adviser Jake Sullivan and China's top diplomat, Yang Jiechi, in Zurich on Wednesday.

Washington will continue to engage with Beijing at a senior level to ensure "responsible competition," Sullivan told Yang, the White House said in a statement.

The fact that the two senior officials flew more than 6,000 km each to the Swiss city yet were unable to set an in-person summit, let alone the date for the virtual talks, showed just how far apart the two sides are despite signs of a thawing in recent weeks.

Wednesday's meeting "followed up on the September 9 phone call between President Biden and President Xi in which the leaders discussed the importance of maintaining open lines of communication to responsibly manage the competition between the United States and the People's Republic of China," the statement said.

Sullivan made clear that while the U.S. will continue to invest in its own national strength and work closely with allies and partners, "we will also continue to engage with the PRC at a senior level to ensure responsible competition," it said.

China's official Xinhua News Agency reported that the meeting was "constructive and conducive to enhancing mutual understanding." The two sides agreed to strengthen strategic communication, properly manage differences, avoid conflict and work together to push relations "back on the right track," the report said.

Yang said Beijing attaches importance to Biden's recent "positive statements," such as that the U.S. has no intention of containing China's development and will not engage in a new Cold War, according to Xinhua.

China opposes using "competition" to define Sino-American relations, Yang said in the report.

The term "responsible competition" that Sullivan used is different from the phrase "strategic competition" the administration was using earlier to describe the relationship with China. The new wording seemed to reflect the agreement between the two presidents in the Sept. 9 call to ensure that competition "does not veer into conflict."

The closed-door talks marked Sullivan's first face-to-face meeting with Yang since their heated exchanges this March in Alaska that also involved U.S. Secretary of State Antony Blinken and Chinese Foreign Minister Wang Yi.

Tensions are rising in the Indo-Pacific, with both sides waging a war of words. Over the weekend, two U.S. aircraft carrier strike groups held drills with a British carrier strike group led by the HMS Queen Elizabeth and a Japanese big-deck ship in waters off Okinawa, Japan.

The Chinese, in response, sent 149 sorties into Taiwan's air defense identification zone in the first four days of October -- up 27% from the number of flights logged in all of September.

On Sunday, the U.S. State Department issued a statement slamming the incursions and talked of deepening ties with a "democratic Taiwan" that angered Beijing.

The U.S. is "very concerned" by China's "provocative" military activity near Taiwan, "which is destabilizing, risks miscalculations, and undermines regional peace and stability," the statement said.

"We will continue to stand with friends and allies to advance our shared prosperity, security, and values and deepen our ties with democratic Taiwan," it concluded.

Chinese Foreign Ministry spokesperson Hua Chunying responded that the U.S. should stop supporting "Taiwan independence" separatist forces and take concrete actions to maintain peace and stability across the Taiwan Strait.

"Taiwan belongs to China, and the U.S. is in no position to make irresponsible remarks," she said. "The relevant remarks by the U.S. side seriously violate the 'one China' principle and the stipulations of the three China-U.S. joint communiques and send an extremely wrong and irresponsible signal."

At the Zurich meeting, Sullivan raised concerns over Chinese actions related to human rights, Xinjiang, Hong Kong, the South China Sea and Taiwan, the White House said.

"Sullivan also raised areas where the U.S. and China have an interest in working together to address vital transnational challenges, and ways to manage risks in our relationship," it noted.