The offer of 14.9 million Taiwan Dollars (USD 470,000) for each family comes seven months after the airline made a similar payout to the families of 48 passengers killed in another crash last July.
TransAsia Airways Flight GE235 crashed on Wednesday last week shortly after take-off from Songshan airport in Taipei with 53 passengers and five crew on board, killing at least 42.
Amateur dramatic dashcam images showed the ill-fated plane hitting an elevated road as it banked steeply away from buildings before crashing into the Keeling River.
One person remains missing after two more bodies were retrieved from the freezing waters on Wednesday.
"We offered an amount of 14.9 million Taiwan Dollars (USD 470,000) as compensation for each person who died in the accident. We hope to reach a settlement with the families," a TransAsia spokeswoman said.
The compensation deal is the result of closed-door discussions held in Taipei on Wednesday with representatives from some of the families.
"We can fully understand that it would be hard for the families to accept it immediately. Still we hope the representatives could take the proposal back and take it into consideration," the spokeswoman said.
She would not say if the proposal had been accepted by the families. Some compensation claims from the July crash remain outstanding as each family had "expected a different amount", the spokeswoman said.
Investigators are still trying to establish what caused last week's crash, but initial reports from the black boxes found the plane's right engine had "flamed out" about two minutes after take-off.
Warning signals blared in the cockpit and the left engine was then shut down manually by the crew for unknown reasons, Taiwan's Aviation Safety Council said on Friday.
Analysts have said the pilots may have caused the crash by turning off the wrong engine.
Following the release of the initial crash findings the Taiwanese flight regulator Civil Aeronautics Administration (CAA) demanded that all 71 of TransAsia's ATR pilots take an oral test on basic operation and emergency procedure of the French-made aircraft.

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