Warbreck councillor Danny Scott told a meeting of the full council he had witnessed riders reaching speeds of around 30mph in some instances, and warned something needed to be done before an injury occurred.
He said in the past he had highlighted the risks poised to pedestrians by pedal bikes on the Prom but "these days we have electric bikes and electric scooters and I am worried about this.
"Statistics are coming through about accidents and deaths of people because of electric scooters and e-bikes."
He added: "I believe with the summer coming up we are seeing more and more of these bikes zipping in and out of the crowds on the Promenade.
"I would like someone to have a look at this please to see what can be done to protect the public, particularly children and of course owners' pets on the Promenade."
Coun Mark Smith, cabinet member for business, enterprise and job creation, said he agreed there had been a rise in the use of e-scooters and bikes in the town.
He said he had witnessed riders "coming from nowhere" and in some instances "spinning across traffic lights".
He said: "People are using this form of transport because it is more economical to get to and from work, but there are other people using them to race around on and they are causing issues.
"I think it is something which needs to be looked at and we will do that with our team, but I also think maybe it is more of a police matter when it comes to enforcement."