The council should not be taking avoidable risks, especially in respect of those who were accessibility challenged, he said.
Woolf said he had received several complaints regarding e-scooter use.
But transport portfolio leader Chris Calvi-Freeman said immediately abandoning the trial was a knee-jerk reaction.
He said the scooter policy would be reviewed at the end of the year.
"People are killed in Wellington by motor vehicles not e-scooters. We need to let the trial run its course and then decide the future of the e-scooters."
Wellington is in the middle of running a six-month trial of two e-scooter provides, Jump and Flamingo.
Lime was fuming when it missed out on a contract.
"We are shocked and disappointed not to have been chosen as one of the operators to take part in Wellington's electric scooter trial," Lime NZ public affairs manager Lauren Mentjox said in March.