As the rescue operation continued into the night, a crane lifted the rear and central sections of the plane from the water, with one body retrieved from inside.
The front part, where 17 people are believed to be trapped, was still in the water.
TransAsia said 16 survivors had been pulled out of the wreckage after the turboprop plane crashed with 58 people onboard. Many of the passengers were mainland Chinese tourists.
Dramatic amateur video footage showed the TransAsia ATR 72-600 hit an elevated road as it banked sidelong towards the Keelung River, leaving a trail of debris including a smashed taxi.
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"I saw a taxi, probably just metres ahead of me, being hit by one wing of the plane. The plane was huge and really close to me. I'm still trembling," one witness told TVBS news channel.
An AFP reporter at the scene said he had seen bodies being pulled from the wreckage into the early evening.
Aviation officials said they had not released the cockpit recording, suggesting it may have come from amateurs monitoring the radio.
"An engine flameout refers to the engine shutting down in flight," said Daniel Tsang, founder of Hong Kong-based aviation consultancy Aspire Aviation.
"The engine stops producing thrust and the combustion process fails and no longer generates any forward propulsion to the aeroplane."
But Tsang told AFP that pilots were "very well trained" to deal with the failure of one engine and the causes of the accident were likely to be more complex.
Today's accident happened just before 11:00 am local time (0830 IST), shortly after Flight GE235 left Songshan airport in northern Taipei en route to the island of Kinmen with 53 passengers and five crew on board.
Six airline officials, including chief executive Peter Chen, bowed in apology at a televised press conference.