Lime is set to roll out additional safety measures just days after a 59-year-old man was the first New Zealander to be killed while riding one of their e-scooters.

The man died in central Auckland on Monday night and within 12 hours of his death, a woman in her 60s was getting off a bus near Auckland's Victoria Park when she was knocked over and left bleeding, her head wedged against a wheel of a bus.

Lime said it was working with Auckland Council and police "to provide all available information".

A spokeswoman said the company would be "rolling out additional safety measures in the coming days".

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"Our service has always included safety education including a 'how to ride tutorial', in-app safety messages, regular communications to riders and 'respect the ride' safety events," she said.

The man's death is now under police investigation.

But Auckland councillor Christine Fletcher is among those again calling for tighter safety regulations and "a complete review" of the rules surrounding e-scooter use.

Fletcher - who was almost knocked over by a Lime scooter last year - says there needs to be a reduction of the speed limit and compulsory helmets.

"One death is too many deaths," she said.

Lime Scooters have been able to take to city streets around the country by gaining the permission of local councils to undertake trials.

The NZ Transport Agency, meanwhile, is responsible for managing the Road User Rule, which governs how e-scooters are used on the roads, while police are responsible for enforcing these road rules.

A NZTA spokesman said he couldn't comment on Monday night's death because it was under police investigation.

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Current rules for e-scooters do not require riders to wear helmets but do require them to ride "in a careful and considerate manner", he said.

This included giving way to pedestrians and mobility scooters, not riding at hazardous speeds and - if on the road - then riding as far left as possible.

"The Government has stated that further regulations for the use of e-scooters, including speed limits and mandatory helmet use, will only be considered after the conclusion of current local authority trials," the spokesman said.

The results from the different trials would be fed into a larger Ministry of Transport study, called Accessible Streets, aiming to encourage more public transport use while also improving safety.

NZTA safety tips for e-scooter use

• Be as safe as possible and be aware of cyclists, other road users and pedestrians who may not hear you approaching.

• NZTA strongly recommends e-scooter riders wear helmets.

• E-scooter riders who do use the road rather than the footpath, are required to keep as far to the left as is practicable for their safety and the safety of others.

• Anyone riding dangerously on any part of the footpath, cycle lanes or road may be subject to police.