China slammed the United States for its "dangerous" decision to congratulate Taiwan's President Tsai Ing-wen on her Wednesday inauguration, as the self-ruled island became the latest flashpoint between the world's two largest economies.

Taiwanese voters handed Tsai a second term with a landslide win in January, a vocal rebuke of China's ongoing campaign to isolate the island.

She was sworn in for another four years at a ceremony on Wednesday in which she called on China to live peacefully alongside a self-ruled Taiwan and for a lowering of tensions.

But a congratulatory note from US Secretary of State Mike Pompeo hailing Tsai's "courage and wisdom" sparked a rebuke from Beijing, which bristles at any formal recognition of Taipei.

"It is extremely wrong, and it's also very dangerous," China's defence ministry said.

Beijing's foreign ministry said it was "extremely indignant" at the message and accused Washington of breaching its diplomatic commitments.

Tsai, 63, is loathed by Beijing because her party views Taiwan as a de facto sovereign state and not part of "one China".

Since she first came to office in 2016, China has rebuffed offers of talks and ramped up economic, military and diplomatic pressure on the island.

'A way to coexist'

Beijing views Taiwan as part of its territory and has vowed to seize it by force if necessary.

Washington diplomatically recognises Beijing but remains a major ally for Taiwan and is bound by Congress to provide arms sales to ensure its defence.

Under President Donald Trump, ties between Taipei and Washington have further warmed as China-US relations plummet.

Beijing envisages a "one country, two systems" model that — like nearby Hong Kong — would allow Taiwan to keep some freedoms while submitting to Chinese mainland rule.