Many passengers were tourists or people traveling to see family ahead of a yearly religious holiday.
Media showed pictures of survivors being led out of the tunnel.
A Taiwan express train with nearly 500 aboard derailed in a tunnel on Friday, killing at least 48 passengers and injuring 66 in the island's worst rail disaster in nearly four decades. "We broke the window to climb to the roof of the train to get out".
The AP reported that a truck somehow fell off a cliff and landed directly in front of the tunnel.
An eight-car passenger train carrying 490 people has derailed in a tunnel just north of Hualien, in eastern Taiwan, killing more than 50 and injuring scores more, according to local authorities.
Images showed an injured passenger carried away on a stretcher, with her head and neck in a brace, while others gathered suitcases and bags in a tilted, derailed carriage as some walked on the train's roof to exit the tunnel.
The National Fire Service said more than 100 people were injured in the crash - Taiwan's worst railroad disaster in more than 70 years.
"The top priority now is to rescue the stranded people", Tsai's office said in a statement.
A train partially derailed along Taiwan's east coast on Friday, with dozens of people feared dead.
An investigation has been launched, and Hualien police have interviewed one person, Weng said.
The accident occurred at the start of the busy annual Tomb Sweeping festival, a long holiday weekend when Taiwan's roads and railways are usually packed.
Taiwan is a mountainous island, and most of its 24 million people live in the flatlands along the northern and western coasts that are home to most of the island's farmland, biggest cities and high-tech industries.
In a tweet, Taiwanese President Tsai Ing-wen said emergency services "have been fully mobilised to rescue & assist the passengers & railway staff affected".
Weng said the speed of the train at the time of impact was not known.
"We will continue to do everything we can to ensure their safety in the wake of this heartbreaking incident".
A collision between two trains resulted in 30 deaths and 112 injuries.
Friday's crash looks set to be one of Taiwan's worst railway accidents in recent decades.
And in 2003, 17 died and 156 were injured after a train on the Alishan mountain railway plunged into a chasm at the side of the track.
The 408 train is one of the fastest deployed on a network that is generally considered safe.
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