Taiwan's shooting down of a drone off the Chinese coast that buzzed a Taiwanese-controlled island was the most "appropriate" thing to do after repeated warnings, and China should exercise restraint, Taiwan Premier Su Tseng-chang said on Friday.

For the first time, Taiwan's military shot down an unidentified civilian drone that entered its airspace near an islet near China's Xiamen city on Thursday, after the government vowed tough measures against a rise in intrusions.

China responded that Taiwan was trying to "hype up tensions" over the incident, which follows the island's complaints of harassment regarding drones from China flying close to the Kinmen islands, as Beijing stages military drills around Taiwan.

Su told reporters Taiwan had repeatedly issued warnings and asked China "not to encroach on our doorstep".

He added, "They repeatedly ignored our warnings to leave and we had no choice but to exercise self-defence and shoot. This is the most appropriate reaction after repeated restraint and warnings."

China should exercise restraint, Su said.

"We will never provoke, and we will do the most appropriate thing to protect our land and our people."

In Beijing, foreign ministry spokesperson Zhao Lijian said Taiwan's ruling party's "attempt to hype up tensions does not mean anything".

Taiwan media cited China's Taiwan Affairs Office as saying in response to the drone's downing that it was "extremely ridiculous" that Taiwan was trying to "hype up confrontation".

The drone was shot down after entering restricted air space near the tiny Lion islet, and crashed into the sea, according to Taiwan's military.

The Kinmen defence command said that on Friday its forces detected two further drones which "quickly" flew back to Xiamen after troops fired flares to warn them away.

Chinese forces have been exercising near Taiwan since early last month, following the visit to Taipei of U.S. House Speaker Nancy Pelosi, which infuriated Beijing.

China views democratically-governed Taiwan as its own territory, despite the strong objections of the government in Taipei.

At least two videos of recent drone trips have circulated widely on Chinese social media, in one of which Taiwanese soldiers were seen throwing stones at the craft.

Su said these videos were made for China's "propaganda at home", adding to the anger of Taiwan's people.

China's foreign ministry on Monday dismissed Taiwan's complaints about drones as nothing "to make a fuss about".

Taiwan fired warning shots at a drone for the first time on Tuesday shortly after President Tsai Ing-wen said she had ordered the military to take "strong countermeasures" against what she termed Chinese provocations.

Taiwan has controlled Kinmen, which at its closest point is a few hundred metres (feet) from Chinese territory, since the defeated Republic of China government fled to Taipei after losing a civil war to Mao Zedong's communists in 1949.

During the height of the Cold War, China regularly shelled Kinmen and other Taiwanese-held islands along the Chinese coast, and while they retain a sizeable military presence they are now also tourist destinations.