ComfortDelGro's flat fare option, which was launched yesterday, has already received 2,000 bookings; and the firm expects the volume to grow further.
'Dynamic pricing', as used by GrabCar and Uber, means private-hire cars are generally cheaper than taxis during off-peak hours and after midnight.
Surge pricing adopted by private-hire apps has drawn flak from some commuters, after fares rocketed during periods of exceptionally high demand.
The fares, which will range from a few dollars to $100, are quoted upfront and could be lower or higher than standard metered rates; depending on demand.
Grab declined to confirm what percentage of the cut it would take and would only say that it would release more details next week.
Singapore's largest taxi operator, ComfortDelGro, has said that it will not implement surge pricing for its taxis for the moment.
Dynamic pricing, also known as surge pricing, will be an additional option for commuters booking a taxi, on top of the current metered rates.
Grab will be rolling out a new taxi service - JustGrab - which will provide fixed upfront fares when booking a taxi but will also be subject to surge pricing.
During major rail breakdowns, commuters have complained of Uber fares exceeding $140 - four to five times that of a usual taxi fare.