The warship was on a "routine mission" on Thursday, Taiwan's defence ministry said, as it traversed the stretch of water that divides the self-ruling island from the authoritarian Chinese mainland.

The waterway bristles with hardware on both sides and China views any sail-by as a breach of its sovereignty.

The US and many other nations say the strait is international waters and Washington regularly carries out so-called "Freedom of Navigation" operations to press the point.

The sail-by comes after Tsai Ing-wen won a second term as president in weekend elections with an increased majority.

The outcome was seen as a forceful rebuke of Beijing's ongoing campaign to isolate the island.

China's leadership had made no secret of its desire to see Tsai turfed out because she and her party refuse to acknowledge their view that Taiwan is part of a "one China".

Beijing regards the island as its territory and has vowed to one day seize it, by force if necessary -- especially if it declares independence.

In Beijing, foreign ministry spokesman Geng Shuang said China "closely followed" the ship throughout its entire journey.

"The Taiwan issue concerns China's sovereignty and territorial integrity, and is the most important, most sensitive issue in China-US relations," Geng said at a regular press briefing.

He said the US must "abide by the One-China principle" in order to "avoid hurting China-US relations and the peace and stability of the Taiwan Strait."

Afer Tsai's re-election, China warned against any move to push the island closer towards formal independence.

Beijing has stepped up military and diplomatic pressure on Taiwan since Tsai came to power in 2016.

The newly commissioned Shandong, China's first domestically built aircraft carrier, sailed through the Taiwan Strait in December just weeks before the election.

Beijing's only other carrier -- the Liaoning -- has passed through the Taiwan Strait several times in recent years, most recently in June.