The defense ministry said the military have set up an ad hoc anti-typhoon center and asked military units to stand by for any rescue missions.
The authorities shut down the popular scenic Kenting beaches in Pingtung, the southern couty expected to bear the brunt of the storm, while fishing boats sought shelters at ports.
The storm's center was at 260 kilometers (156 miles) south-southwest of Oluanpi, the southernmost tip of Taiwan at 06:00 pm (1000 GMT), the Central Weather Bureau (CWB) said.
Packing center winds of up to 100 kilometers an hour, Conson was moving north-northeast at an hourly speed of 11 kilometers.
"The tropical storm has gained power over the past three hours and may upgrade into a typhoon," a CWB official warned.
The storm, already threatening the south and east of the island, is forecast to lash southern Taiwan Wednesday, the official said.
The bureau warned of heavy downpours in southern areas, urging residents to take precautions against floods and landslides.
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