Photos and video taken by Chinese drones of the Kinmen islands have been circulating on both Taiwanese and Chinese social media, with one video showing Taiwanese soldiers hurling rocks at one to drive it off.

While visiting air force facilities in offshore Penghu islands, President Tsai Ing-wen said China had used "greyzone" tactics such as drone intrusion to continue its "military intimidation" against Taiwan.

"I want to tell everyone that the more provocative the enemy is, the more calm we need to be... we will not provoke a war and we will restrain ourselves, but that does not mean that we will not take countermoves," she told the troops stationed in the archipelago in the Taiwan Strait.

Tsai added that she had ordered the defence ministry "to take necessary and strong countermeasures at an appropriate time to defend the security of our airspace".

Asked to comment on the videos Monday, Chinese foreign ministry spokesman Zhao Lijian said the incursions were not "anything worth making a fuss about" as the drones were "flying around Chinese territory".

But that response triggered an angry riposte from Taipei, which compared the drone harassment to the acts of a "thief".

"Those who come uninvited are called thieves, whether they are breaking through the door or peeping from the air, the people of Taiwan do not welcome such thieves," Taiwan's foreign ministry said in a statement late Monday.

"The authoritarian expansionist government of the Chinese Communist Party has always made harassing other countries a daily routine, and therefore its title of a 'regional troublemaker' is well deserved."

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

Drone incursions over Kinmen have increased at the same time Beijing embarked on a show of force in retaliation for US House Speaker Nancy Pelosi's visit to Taiwan earlier this month.

For a week after Pelosi's visit, China sent warships, missiles and fighter jets into the waters and skies around Taiwan, its largest and most aggressive exercises since the mid-1990s.

It is not clear who is flying the drones from the Chinese mainland.

Kinmen lies just a few kilometres off China's coast, meaning a civilian could feasibly fly a commercial drone that distance.

However China has also stepped up so-called "greyzone" tactics against Taiwan in recent years to pressure the island.

"Greyzone" is a term used by military analysts to describe aggressive actions by a state that stop short of open warfare and can use civilians.

Civilian Chinese fishing and sand dredging vessels, for example, have increasingly entered waters around Taiwanese outlying islands in recent years.

China has also ramped up incursions by warplanes into Taiwan's air defence identification zone, an area it previously tended to avoid.

Taiwan's defence ministry has so far only fired flares to warn off the drones but it has said it will take "necessary countermeasures", including shooting down the drones if needed.