TAIPEI (Reuters) - A U.S. warship sailed through the Taiwan Strait on Thursday, the island’s defense ministry said, less than a week after Taiwan President Tsai Ing-wen won re-election by a landslide on a platform of standing up to China which claims the island.

The ship sailed in a northerly direction through the sensitive waterway and Taiwan’s armed forces monitored it throughout, the ministry said in a brief statement on Friday, describing the sailing as an “ordinary mission”.

“People can rest easy,” it added.

Taiwan is China’s most sensitive territorial and diplomatic issue and Beijing has never ruled out the use of force to bring the island under its control. The narrow Taiwan Strait which separates the island from China is a frequent source of tension.

China sailed its latest aircraft carrier, the Shandong, through the waterway twice in the run-up to Taiwan’s election last Saturday.

Taiwan denounced that as attempted intimidation.

The U.S. Navy said the Ticonderoga-class guided-missile cruiser USS Shiloh had completed a transit of the Taiwan Strait, without giving details. The United States has been conducting sporadic missions through the strait in the last two years.

In Beijing, Chinese Foreign Ministry spokesman Geng Shuang said the government also “closely watched” and monitored the ship’s passage, urging the United States to “appropriately deal with the Taiwan issue in a way that doesn’t hurt Sino-U.S. relations and peace and stability in the Taiwan Strait”.

Washington has no formal ties with Taiwan but is bound by law to provide the island with the means to defend itself and is its main source of arms.

Meeting the de facto British ambassador to Taiwan later on Friday, Taiwan President Tsai Ing-wen said the island would ensure peace in the Taiwan Strait.

“As a responsible member of the international community, Taiwan will continue to dedicate itself to protecting peace and stability in the Taiwan Strait,” the presidential office cited Tsai as telling Catherine Nettleton.

Under the Trump administration, the United States has made bolstering its defense and other ties with Taiwan a priority, in spite of Chinese anger.

The top U.S. diplomat in Taiwan, Brent Christensen, told a forum in Taipei on Friday that his office’s theme for this year was “real friends, real progress”, and took what appeared to be an indirect dig at China.

“Perhaps this concept sounds simple, but it is important to consider its significance within the current context,” said Christensen, director of the American Institute in Taiwan.

“Some use the cover of friendship to dominate and manipulate; promising mutual benefit but instead delivering extortion; exporting problems rather than solutions,” he added.

Christensen said the United States this year will seek to further Taiwan’s engagement in the world, something the island has found difficult due to China blocking Taiwan’s participation in most international organizations.

“The United States and Taiwan are members of the same family of democracies,” he added.