Four teenage girls have been arrested after allegedly leading police on three separate pursuits in a stolen car through Sydney's west on Thursday night.

Three girls - aged 13, 15 and 17 - were passengers in the Nissan Altiva, which was being driven by an unlicensed 16-year-old.

Police said the car had been reported stolen earlier in the week.

At 10pm on Thursday, police were conducting random breath tests on Doonside Road, Doonside, when the car allegedly failed to stop when directed.

A police police began but was ended a short time later after police lost sight of the car.