The quake hit just before 8:00am local time (0000 GMT), with the United States Geological Survey (USGS) putting the epicentre 18 kilometres (11 miles) south of Taiwan's Hualien City, at a depth of 34.8 km.
Japan's Meteorological Agency issued a warning for tsunami waves as high as three metres (10 feet) for remote Japanese islands in the region, including Miyakojima island.
In Taiwan, authorities issued a tsunami warning via text message "to remind people in coastal areas to be vigilant and take strict precautions and pay attention to the dangers caused by sudden surges in waves".
The initial earthquake was felt across Taiwan, with AFP reporters from the southern Pingtung county to the north in Taipei reporting strong shaking sensations.
The aftershocks -- which included a 6.5-magnitude earthquake near Hualien according to Taipei's weather agency -- were also felt in Taipei.
In the capital, the metro briefly stopped running but appeared to have resumed within an hour, while residents received warnings from their local borough chiefs to check for any gas leaks.
"I wanted to run out but I wasn't dressed. That was so strong," said Kelvin Hwang, a guest at a downtown hotel who sought shelter in the lift lobby on the ninth floor.
Officials said the earthquake was the strongest felt on the island in decades.
"The earthquake is close to land and it's shallow. It's felt all over Taiwan and offshore islands," said Wu Chien-fu, director of Taipei's Central Weather Administration's Seismology Center.
"It's the strongest in 25 years since the (1999) earthquake," he told reporters.
A 7.6-magnitude quake hit Taiwan in September 1999, killing around 2,400 people in the deadliest natural disaster in the island's history.
Wu warned that authorities are not ruling out that "there will be earthquakes with magnitude of 6.5 to 7 in three days which will be relatively close to the land".
"The public should pay attention to relevant warnings and messages and be prepared for earthquake evacuation."
- Earthquake territory -
Taiwan is regularly hit by earthquakes as the island lies near the junction of two tectonic plates, while nearby Japan experiences around 1,500 jolts every year.
To Taiwan's west, the Philippines also issued a tsunami warning and called for the evacuation of coastal areas.
Coastal areas in the northern provinces of Batanes, Cagayan, Illocos Norte and Isabela "are expected to experience high tsunami waves" based on tsunami wave models, the state seismological agency said.
In Japan, a banner on national broadcaster NHK said "Evacuate!"
"Tsunami is coming. Please evacuate immediately," an anchor on NHK said. "Do not stop. Do not go back."
Live TV footage from the Okinawa region's ports, including Naha, showed vessels heading out to sea, possibly in efforts to protect their ships.
Flights were suspended at Okinawa's main airport as a precautionary measure, a transport ministry official told AFP.
The vast majority of quakes around the area are mild, although the damage they cause varies according to the depth of the epicentre below the Earth's surface and its location.
The severity of tsunamis -- vast and potentially destructive series of waves that can move at hundreds of miles (kilometres) per hour -- also depends upon multiple factors.
Japan's biggest earthquake on record was a massive 9.0-magnitude undersea jolt in March 2011 off Japan's northeast coast, which triggered a tsunami that left around 18,500 people dead or missing.
The 2011 catastrophe also sent three reactors into meltdown at the Fukushima nuclear plant, causing Japan's worst post-war disaster and the most serious nuclear accident since Chernobyl.
Japan saw a major quake on New Year's Day this year, when a 7.5-magnitude earthquake hit Noto Peninsula and killed more than 230 people, many of them when older buildings collapsed.
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