Australia's top spy agency has expressed "great concern" over material leaked by the fugitive US intelligence worker Edward Snowden and has carried out an audit to ascertain what Australian information Snowden might have.

Top-secret documents from the Defence Signals Directorate, now known as the Australian Signals Directorate (ASD), show Australian spies targeted the mobile phones of Indonesia's president, his wife and senior officials in 2009.

The ASD slide, published by the ABC and Guardian Australia, has prompted Indonesia to recall its ambassador to Australia in protest.

"Certain material that has been released by Snowden that is now in the public realm is of very great concern," the director general of the Australian Security Intelligence Organisation (Asio), David Irvine, told a Senate estimates hearing on Monday.

"That material is Australian material. It is obviously of very great concern to the Australian government."

Irvine said there was "good collaboration and productive collaboration" between Australian intelligence agencies and agencies from friends and allies around the world.

But he said Asio had conducted an audit of intelligence it has shared with foreign agencies to assess what sort of Australian material Snowden might have.

"It stands to reason that is something we would do," Irvine said. He would not comment on the nature or scope of the intelligence material.

"We have a good idea of what information we have shared with other allied and friendly agencies, but I won't go into that."

The Greens senator Scott Ludlam used the hearings to ask the attorney general, George Brandis, if the ASD could be allowed to appear before a Senate estimates hearing. The top-secret agency currently does not do so.

Brandis said the ASD was an agency within the Department of Defence, but he did not expect the new government would change the current practice.