The Department for Transport (DfT) has announced a wide-ranging review of transport laws that could lead to them being allowed on UK roads for the first time.
Scooters with electric motors can exceed 30mph and are legal on roads in several European countries and US states.
However, IAM RoadSmart said riders could be endangered by sharing streets with faster traffic.
It said such a move would be "bad news for road safety".
The group said it will lead to many people riding them on roads alongside bigger and faster vehicles – "and will put individuals, including the scooter users themselves, in great danger".
Neil Greig, its Scotland-based director of policy and research, said: “Electric scooters are simply not safe enough to be on our roads alongside full-size vehicles.
"Putting them together in close proximity is a dangerous cocktail and could potentially be tragic.
“Mixing with pedestrians is also potentially very unsafe in shared areas.
"As with cycling, the answer probably lies in dedicated safe infrastructure [separate lanes] for vulnerable road users.
"Allied to that, there is an urgent need for rider training and clarification of their legal status.”
Cycling and walking group Sustrans said e-scooters should be limited to 15mph (25kph) if permitted on cycle paths.
Chief executive Xavier Brice said: “We need to be doing everything we possibly can to enable more people to walk, cycle, scoot or wheel (in wheelchairs or mobility scooters) for short journeys.
"The use of electric scooters is rising in the US and elsewhere and it’s important the law keeps up with the pace of change.
"Electric scooters, like electric bikes, widen choice and early evidence from the States suggests they can appeal to people who wouldn’t usually cycle - albeit without providing all of the benefits to health of walking and cycling.
"We welcome the fact the DfT is considering whether to legalise electric scooters - however, the needs and safety of everyone, including pedestrians and other vulnerable road users, must be considered before any change in the law.
"In particular, there must be clear limitations on power and speed.
"We would be firmly opposed to any proposals which would allow electric scooters or electric bikes to exceed 25kph under motorised power while retaining the right to use cycle facilities."
The Scottish Government said it was looking at the safety of electric scooters.
A spokesperson for its Transport Scotland agency said: “As the popularity and prevalence of e-scooters and other forms of micro-mobility increases globally, we are keen to understand trends across a range of issues, including the safety of both the user of the scooter and other road users.
"We will continue to monitor trends as a matter of course to inform future policy.”
Electric hire firms such as Lime and Bird have set up in competition with cycle rental schemes in other countries.
Bird has also launched a trial on private land at Queen Elizabeth Olympic Park in east London
A 15-year-old boy had six penalty points imposed on his future driving licence last October after being prosecuted for riding an electric scooter at high speed in a public place.
Richard Corbett, head of Bird in the UK, said electric scooters reduced congestion and pollution.
He said: "Cities around the world are already reaping the benefits of innovative forms of transport such as electric scooters."
Lime UK general manager Jaanaki Momaya said: "Last year, we helped hundreds of thousands of residents in Paris make journeys using our e-scooters.
"We hope reform of the existing legislation will one day allow us to offer this service to people in cities across the UK."
The DfT said it has no immediate plans to legalise electric scooters, and advised retailers to be clear to customers about where they can use them.
Future of mobility minister Jesse Norman said: "We are at a potentially pivotal moment for the future of transport, with revolutionary technologies creating huge opportunities for cleaner, cheaper, safer and more reliable journeys.
"Through this strategy, the Government aims to take advantage of these innovations; connecting more people and bringing big benefits we hope for both the economy and the environment."
The UK Government is also launching a competition for up to four new "future mobility zones", which will receive a share of £90 million to test ideas to improve journeys.
This is expected to include more streamlined payment systems, more accurate travel updates and the use of innovative forms of transport, with the aim of making travel in towns and cities more convenient, reliable and cheaper.