Telstra has been ordered to audit its priority assistance systems after two seriously ill people died when their landlines failed.

It follows an investigation by the communications watchdog which revealed Telstra was aware both customers needed a working landline due to their life-threatening, chronic health conditions.

The Australian Communications and Media Authority says it is not clear if the communications giant could have changed the "tragic outcome" but priority assistance was "critical to ensure customers with life-threatening conditions are provided with swift assistance".

The investigation revealed Telstra failed to provide information about its system eight times when customers asked about medical assistance in 2017, and nine times when people were inquiring about the service.

ACMA's acting chair Creina Chapman says the authority is "deeply concerned" with Telstra's "failure to comply with its priority assistance obligations".

The telco is the only provider required to offer customers priority assistance under license conditions which demand it provide information about eligibility and registration to relevant customers.

It must also follow emergency request procedures for customers with a life-threatening health condition who are unregistered but have an urgent need for a working telephone.

The audit will review the training and scripts provided to Telstra staff, as well as previous complaints about the service, before delivering a report to ACMA.