A newly-appointed police commissioner is facing his first hot-seat challenge, having to explain why permission was given for a neo-Nazi rally outside a state parliament.

Barely six weeks into his new job, NSW top cop Mal Lanyon has vowed to get to the bottom of a command-level decision to allow the gathering in Sydney's Macquarie Street on Saturday morning in the wake of laws banning the incitement of racial hatred.

The protest drew the immediate ire of Premier Chris Minns and Jewish community groups, after a group of several dozen black-clad men draped a large banner across the gates of NSW parliament carrying the slogan "Abolish the Jewish Lobby".

It's believed those involved were members of the National Socialist Network, which has staged numerous protests in capital cities and towns

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