Police said the blast which hit the train late Thursday as it was pulling into a station appeared to have been caused by a pipe bomb.
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Of those injured -- 14 male and 11 female -- five were in critical condition, according to the National Police Agency.
"We are currently conducting a full investigation," Wang Pao-chang, head of the agency's Taipei branch, told reporters.
"We are preliminarily ruling it out as a terrorist attack," he said, adding that so far there had been no claim of responsibility for the attack.
Police said a 47-centimetre steel pipe filled with explosive material appeared to be the cause of the blast.
Wang said it was a "roughly made" improvised explosive.
A red bag found in the carriage's toilet was also believed to be connected to the case.
Premier Lin Chuan said the blast was caused by someone with "malicious intent".
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Local media quoted eyewitnesses saying they had seen a man carry a black rectangle-shaped object onto the train.
Images from inside the train carriage showed shattered glass on the floor and part of a side wall blackened by flames.
Passengers rushed off the train once it reached the station, many of them suffering from burns.
"I saw fire from the lights and I heard a sound and my hair was on fire," one woman told a local news channel.
The last major attack on Taipei's public transit was when a college student killed four people in a stabbing spree in 2014 on the metro, shocking the island and prompting a security overhaul.
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