Two United States warships have sailed through the Taiwan Strait, the American navy has said, the first such transit since China staged unprecedented military drills around the island.

In a statement, the US Navy said the transit "demonstrates the United States' commitment to a free and open Indo-Pacific".

Tension in the Taiwan Strait soared to their highest level in years this month after US House Speaker Nancy Pelosi visited Taipei.

Beijing reacted furiously, staging days of air and sea exercises around Taiwan. Taipei condemned the drills and missile tests as preparation for an invasion.

Taiwan lives under constant threat of an invasion by China, which claims the self-ruled, democratic island as part of its territory to be seized one day - by force if necessary.

A general view of the USS Antietam in waters off the Philippines in 2016

Washington diplomatically recognises Beijing over Taipei, but maintains de facto relations with Taiwan and supports the island's right to decide its own future.

The US 7th Fleet said the pair of Ticonderoga-class guided-missile cruisers - the USS Antietam and the USS Chancellorsville - conducted the "routine" transit this morning "through waters where high seas freedoms of navigation and overflight apply in accordance with international law".

"These ships transited through a corridor in the Strait that is beyond the territorial sea of any coastal State," a statement said.

"The United States military flies, sails, and operates anywhere international law allows."

The 7th fleet is based in Japan and is a core part of Washington's navy presence in the Pacific.

Read more: The Taiwan Strait - A history of crises

The US and Western allies have increased "freedom of navigation" crossings by naval vessels of both the Taiwan Strait and South China Sea to reinforce the concept that those seas are international waterways, sparking anger from Beijing.

China's military has said it is monitoring the US vessels, maintaining a high alert and ready to defeat any provocations.

Washington has said its position on Taiwan remains unchanged and has accused China of threatening peace in the Taiwan Strait, using the visit by Ms Pelosi as a pretext for military exercises.

China's drills included firing multiple ballistic missiles into waters off Taiwan, some of the world's busiest shipping routes, which was the first time Beijing has taken such a step since the mid-1990s.

Taiwan staged its own drills, simulating a defense against invasion, displaying its most advanced fighter jet in a rare nighttime demonstration.

Sabre-rattling towards Taiwan has become more pronounced under Chinese President Xi Jinping.