TAIPEI—China has launched “around-the-clock” military drills and, for the first time, announced that it had deployed its coast guard around Taiwan’s main island, following warnings from Taiwanese officials that such actions were likely in response to a major speech by its new president last week.

The drills were seen as a response to a speech by President Lai Ching-te of Taiwan, who said last week that China had “no right to represent” the island.