The issue was discussed at the authority’s transport delivery overview and scrutiny committee meeting on Monday.
Councillor Leslie Kay said the scheme needed to consider safety, having witnessed ‘”reckless cycling” in pedestrian areas.
But councillor Liz Clements said she supported the scheme and would be against any measures that discouraged cycling.
She said: “Because of the number of complaints I get from residents in my ward, I have not been a great fan of the e-scooters because I have some safety concerns about them.
“But I’ve come round to them because I’ve been presented with data that showed they were a significant factor in mode shift, and a lot of the journeys that are being made on e-scooters would otherwise be done by private car.”
While supportive of the scheme, Clements said she also shared concerns about the lack of a proper regulatory framework for e-scooters, which she hoped would be resolved by the government instead of continuing to extend pilot schemes.
She added: “We need these micro-mobility schemes available to give people other options than just driving vehicles.”