Australians cannot have it both ways in wanting their government simultaneously to respect their privacy and also to protect them from terrorist attacks, says former prime minister Julia Gillard.

But Ms Gillard, who was deputy to former prime minister Kevin Rudd when the government allegedly monitored the phone calls of Indonesian President Susilo Bambang Yudhoyono and his wife, told CNN on Friday that she believed Prime Minister Tony Abbott should review Australia's national security procedures.

In an interview with high-profile CNN host Christiane Amanpour, Ms Gillard said that Australians needed to appreciate the "difficult judgments" of national security.

"On the one hand Australians would rightly say to their government if there was a terrorist attack ... why didn't you know, why didn't you collect the intelligence, why didn't you stop it?" Ms Gillard said.