In a statement, the ACMA said its directive followed an investigation in 2017 into the cases of two customers with chronic health conditions who were unable to use their Telstra landline services.
While neither of these customers was registered for priority assistance, both had revealed their condition and the fact that they needed a working telephone service, the ACMA said. Both are now dead.
"Following these events, our initial focus is to address the underlying issue, namely the robustness of the system," said ACMA acting chair Creina Chapman.
The ACMA said that in cases it had investigated Telstra avoided providing information about priority assistance on eight occasions to customers who made inquiries.
The company also did not implement emergency medical request procedures - which are laid down in its priority assistance policy - on nine occasions when inquires were made about the two services.
The telco has now begun an independent audit which will review training and scripts provided to Telstra staff, as well as past customer complaints about priority assistance.
"We’ll be taking a very close look at the results of the independent audit. If we still have concerns with Telstra’s priority assistance services we’ll step in and ensure they’re addressed,’ Chapman said.