Indonesia called in the chief US diplomat in Jakarta this week over the spying allegations, while China on Thursday demanded an explanation from the United States after the Sydney Morning Herald newspaper reported Australian embassies across Asia were part of the US espionage operation.
News of Australia's role in a US-led surveillance network could damage relations with Indonesia, Australia's nearest Asian neighbour and an important strategic ally, Reuters reported.
"Indonesia's Foreign Minister Marty Natalegawa has demanded an explanation from the Australian ambassador in Jakarta about the existence and use of surveillance facilities in the Australian embassy here," Indonesia's Foreign Ministry said in a statement.
"The reported activities absolutely do not reflect the spirit of a close and friendly relationship between the two neighbours and are considered unacceptable by the government of Indonesia."
Australia confirmed its ambassador to Indonesia had been called in to "discuss Indonesia's concerns about media allegations of intelligence activity by Australia", saying the ambassador "took careful note of the issues raised".
Chinese Foreign Ministry spokeswoman Hua Chunying again expressed concern about the reports, saying Beijing was asking Canberra for "clarification".
The Sydney Morning Herald said its reports were based on US whistleblower Edward Snowden and a former Australian intelligence officer.
Snowden leaks to other media have detailed vast intelligence collection by the US National Security Agency (NSA) on allies, including German Chancellor Angela Merkel, prompting protests and a US review of intelligence gathering.