Telstra customers across Australia are reporting difficulties making calls and connecting to the internet on their mobile devices, with both 3G and 4G networks appearing to be affected.

NSW Police said the outages could be affecting people trying to call triple zero (000) or the Police Assistance Line (131 444).

"The advice we have received indicates Telstra customer mobile phone calls to Triple Zero (000) should automatically be connected via another carrier; however, if you are experiencing problems use a landline," they said in a statement at 12.14pm.

Aussie Outages' live outage map, which shows complaints about network problems across all major capital cities, was reporting more than 10,000 incidents about 10am. Complaints started rolling in on social media about the same time, with hundreds of Telstra customers taking to Twitter to report an inability to phone out.