PENGHU, Aug 30 (Reuters) - Taiwan fired warning shots at a Chinese drone which buzzed an offshore islet on Tuesday (Aug 30) shortly after President Tsai Ing-wen said she had ordered Taiwan's military to take "strong countermeasures" against what she termed Chinese provocations.

It was the first time such warning shots have been fired during a period of heightened tensions between China and Taiwan. Beijing views the island as its own territory, while Taiwan strongly disputes China's sovereignty claims.

The drone headed back to China after the shots were fired, a military spokesperson said.

Taiwan has complained of Chinese drones repeatedly flying close to small groups of islands it controls near China's coast as part of military drills by Beijing, most recently by the Kinmen islands.

China has conducted exercises around Taiwan after US House of Representatives Speaker Nancy Pelosi visited the island this month against Beijing's wishes.

Kinmen defence command spokesman Chang Jung-shun said the live rounds were fired at the drone which had approached Erdan islet just before 6pm local time, with flares being used previously. The drone then flew off back to China, he said.

There was no immediate response from China. On Monday, the Chinese Foreign Ministry had dismissed Taiwan's complaints about the drones as nothing "to make a fuss about".

US officials, speaking on the condition of anonymity, said it appeared China was using the drones to harass the Taiwanese rather than escalate the situation.

But they added they were monitoring the situation closely and were concerned about accidents in general.

Footage of at least two drone missions showing Taiwanese soldiers at their posts, and in one case throwing rocks at a drone, have circulated widely on Chinese social media.

Speaking earlier on Tuesday while visiting the armed forces on the Penghu islands, Tsai criticised China for its drone and other "grey zone" warfare activity.

She did not elaborate on what countermeasures she had ordered the defence ministry to take.

"I want to tell everyone that the more the enemy provokes, the more calm we must be," Tsai told naval officers. "We will not provoke disputes, and we will exercise self-restraint, but it does not mean that we will not counter."

The Kinmen islands are at their closest point just a few hundred metres from Chinese territory, opposite China's Xiamen and Quanzhou cities.