Taiwan's defence minister warned Tuesday that enemy threats were growing daily after China's aircraft carrier and a flotilla of other warships passed south of the island in an exercise as tensions rise.

After sailing south of Taiwan itself, the Liaoning and five other warships on Monday passed the Taiwan-administered Dongsha Islands in the South China Sea also claimed by Beijing, according to Taiwan's defence ministry.

The naval drills are seen as a show of strength by Beijing as its relations worsen with Taiwan and the United States, following a protocol-breaking telephone conversation between Taiwanese President Tsai Ing-wen and US President-elect Donald Trump.

Chinese media had earlier reported that the carrier was headed for the Pacific on exercise for the first time along with its escort ships.

It was the latest in a series of recent exercises staged by China, after its military aircraft passed near Taiwan on December 10 for the second time in less than a month.

Taiwan's defence minister Feng Shih-kuan said Tuesday, during a promotion ceremony for generals, that threats from the enemy were growing daily.

"I ask for strict training... We train the soldiers so they can not only survive the war but also destroy the enemies and accomplish their missions," he said, without referring to China by name.

"The threat from our enemy is increasing day by day. We need to maintain combat vigilance at any time. This is my expectation of you all."

Feng confirmed that Taiwan sent RF-16 reconnaissance aircraft to monitor the Chinese warships.

His ministry estimated that the Liaoning would arrive at a base in China's southern island province of Hainan around Tuesday evening.

"The ministry has been tracking the Liaoning carrier's movements so the public can rest assured... and will closely monitor its movements in the future," it said in a statement.

Recently the Liaoning has been involved in exercises in the Yellow Sea, with J-15 fighter jets taking off from it and conducting air refuelling and combat drills, according to China's state news agency Xinhua.

Earlier in the month the Liaoning led large-scale exercises in the Bohai Sea that included live ammunition for the first time.

Ties between Taiwan and China have turned increasingly frosty since Tsai's election victory in January. Beijing has cut off official communication with her government, which took office in May, after it refused to publicly accept the "one China" concept.

Under Taiwan's previous government the two sides had stuck to the "1992 consensus", in which they agree there is only one China without specifying which is its rightful representative.

China poses the main military threat to self-ruled Taiwan. Beijing sees the island as part of its territory awaiting reunification -- by force if necessary -- even though the two sides have been ruled separately since the end of a civil war in 1949.

It has more than 1,000 missiles aimed at the island, according to Taiwan's defence ministry.