There have been hundreds of scooters distributed around the CBD, South Bank, Fortitude Valley and other inner-city suburbs, with a 251 per cent growth in daily trips since last Friday.

Lime Asia Pacific head Jeff Roberts said there were almost 20,000 unique riders in Brisbane.

"It is fantastic to see our fleet being fully utilised by the Brisbane community and there is a high demand for us to expand our services beyond the inner-city," he said.

The company wants to work with Brisbane City Council to increase the number of scooters available.

"Due to the sheer number of rides each scooter is doing each day, many have to be retrieved early than usual to be recharged," Mr Roberts said.

"Brisbane City Council has been so supportive of Lime since launching and we will continue to work closely with all levels of government to mitigate any issues should they arise."

However, the popularity of Limes scooters has not diminished people's enthusiasm for Brisbane City Council's CityCycle scheme, with a record number trips on the hireable bikes last month.

In November, there was a new monthly trip record of 71,663 trips taken on CityCycle.

It is understood multiple companies have approached the council seeking to roll out electric scooters.

The council would envisage only one scooter company operating in Brisbane going forward, and that operator would be chosen by a competitive tender process.

Lime's electric-powered scooters can travel at speeds of up to 27km/h and can be found and hired using a map on its mobile app, rather than left at a docking station, such is the case with CityCycles.

Transport and Main Roads wrote to Lime to warn users would be breaking several laws if they took one of the "illegal" scooters for a spin during a planned trial, with fines of up to $10,444.

However, Transport Minister Mark Bailey later intervened to announce Lime would be offered a temporary exemption during a review of Queensland's laws and regulations, which was expected to be completed by Christmas.

Meanwhile, Bennett & Philp Lawyers director Trent Johnson said the person who hired a Lime scooter would be liable for any crashes they caused while riding.

"At present, we are seeing users of the scooters weaving between pedestrians and I have no doubt that we will see accidents and injuries before the scheme trial ends," he said.

Mr Roberts said he wanted to remind riders to keep the safety of themselves and the community in mind.

"Safety will always be Lime's number one priority and it has been so encouraging to see so many Brisbane riders using the supplied helmets," he said.