Typhoon Dujuan, packing maximum winds of up to 209 kilometres (130 miles) per hour, was 560 kilometres southeast of Hualien county at 2:30 pm (7pm NZDT), and lay around 350 kilometres from the Japanese island of Ishigaki.
"It's at the upper limit of a moderate storm, and we do not rule out that it gets stronger," a spokesman from Taiwan's weather bureau told AFP.
Ferry operators increased trips to move people from Green Island and Orchid Island, popular with tourists, and services will be suspended later Sunday.
A total of nearly 3,000 people were being evacuated from the two islands, the local tourism bureau said.
Dujuan is set to hit Ishigaki at around midday on Monday, and make landfall in Taiwan later the same evening. The storm is on course to hit mainland China from Tuesday after moving through Taiwan.
Japan's meteorological agency has warned it could trigger waves 13 metres (42 feet) high when it strikes the country.
So far there have been no reports of damage or injuries in connection with the typhoon, but "winds are getting stronger now", an Ishigaki official told AFP by phone.
At least three flights were cancelled, Japanese news reports and airline officials said, and the country's meteorological agency warned of possible landslides, high waves and heavy rain.
- AFP

