Indonesian hackers are vowing a fresh wave of cyber attacks against Australia in retaliation for the spying affair, this time targetting government websites including intelligence agency ASIO.

Nearly a week after hackers launched a series of indiscriminate attacks on Australian websites including charities, small businesses and even a major hospital, hackers are vowing to start a second wave on Friday night.

The hackers have used a number of Indonesian websites to threatening "denial of service" attacks - which crash websites - against the Australian government. Early Friday evening the ASIO website was working normally, as were other major government websites.

The promise to focus this time on government websites came partly in response to a backlash from the Australian branch of hacker activist group Anonymous.

A message and video posted by Anonymous Australia on the website Cyber War News warned of a counter attack by Australian hackers if the Indonesians continued to target innocent private websites.

"You have defaced many innocent Indonesian websites in an effort to protest against the Australian government and their spy agency ASIO," the video states. "Innocent businesses should not be attacked ... We bid you as a fellow brother to focus on your main target, governments and spy agencies. Leave the innocent bystanders out of this.

"If you choose to disagree then you should feel the full wrath of our fellow legion."

Anonymous Australia says it will help the Indonesia hackers if they restrict their attacks to government websites.

Contacted via email and Facebook, hackers have told Fairfax Media they are angry at the Australian government's failure to apologise over reports that the Australian embassy in Jakarta has been used to house electronic surveillance equipment.

But some have acknowledged it was a mistake to attack random websites including small businesses and charities.

Those attacks defaced homepages with messages such as: "This is not a joke or a dream, this is f---ing reality. Stop illegal spying on Indonesian."

The attacks follow Fairfax Media reports that Australian embassies across Asia, including the Jakarta embassy, were used for electronic surveillance in an operation unknown to most embassy staff.