The USS Milius (DDG69) guided-missile destroyer arrives at the US naval base in Yokosuka, Japan. File/Reuters

A US warship sailed through the strait separating Taiwan and China on Tuesday, the navy said, the first such passage since leaders from the two rival superpowers held a video summit.

The passage through the Taiwan Strait by the Arleigh Burke-class guided missile destroyer USS Milius was a routine transit, the US Seventh Fleet said.

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The voyage, the 11th declared freedom of navigation exercise of the year, "demonstrates the US commitment to a free and open Indo-Pacific," it said in a statement.

US President Joe Biden and China's Xi Jinping traded strong warnings on the future of Taiwan.

The latest transit came after US President Joe Biden and China's Xi Jinping traded strong warnings on the future of Taiwan at a virtual summit earlier this month.

Chinese state media reported after the summit that Xi cautioned Biden that encouraging Taiwanese independence would be "playing with fire".

US warships periodically conduct exercises in the strait, often triggering angry responses from Beijing, which claims Taiwan and surrounding waters as its own territory.

The US and many other countries view the route as international waters open to all.

Meanwhile, China has warned Taiwanese firms against supporting the island's independence, hours after state media said a Taiwanese conglomerate was fined by mainland regulators as tensions flare between Taipei and Beijing.

Analysts said the move could ratchet economic pressure on Taiwanese companies operating in China — and the local mainland firms that invest in them.

Beijing claims self-ruled democratic Taiwan as part of its territory to be re-taken one day, by force if necessary.

It has intensified military, diplomatic and economic pressure on Taiwan since President Tsai Ing-wen's 2016 election, as she sees the island as "already independent" and not part of its "one China".

Beijing "would never allow people who support 'Taiwan independence' and damage cross-strait relations to make money on the mainland," the Taiwan Affairs Office (TAO) said in a statement issued late Monday.

It was responding to a report on the official Xinhua news agency that Taiwan's Far Eastern Group was fined in China over its investments in several Chinese provinces for violating local regulations.