Vice President Kamala Harris discussed challenges posed by China with French President Emmanuel Macron and German Chancellor Olaf Scholz and agreed to remain closely aligned during meetings with the leaders in Munich, the White House said on Friday.

Harris "discussed challenges posed by the People's Republic of China, including the importance of upholding the rules-based order, and agreed to remain closely aligned," the White House said in a statement.

The meetings of the U.S. vice president with the European leaders, held alongside the Munich Security Conference, come amid a bitter dispute between China and the United States over the U.S. military's shooting down of what it said was a Chinese spy balloon off the coast of South Carolina early this month. China says the balloon was for monitoring weather.

Harris defended the United States' handling of the balloon incident and the shooting down of three other unidentified objects.

"It needed to be shot down because we were confident that it was used by China to spy on American people," Harris told MSNBC.

Separately, the Pentagon's top China official, Deputy Assistant Secretary of Defense Michael Chase, arrived in Taiwan, two sources familiar with the matter said on Friday, beginning a visit that could further exacerbate tensions between Beijing and Washington.

Although the United States, like most countries, has no formal diplomatic ties with Taiwan, it is the island's most important arms supplier and the two have a close security relationship.

China, which views Taiwan as its own territory, has repeatedly demanded that foreign officials not visit the democratically governed island.

U.S. diplomatic communications with China remain open after the shooting down of the Chinese balloon, but contact between the countries' militaries remained shut down, the White House said earlier on Friday.

China cut several military-to-military communication channels and other areas of bilateral dialog after an August visit to Taiwan by then-U.S. House of Representatives Speaker Nancy Pelosi.