Prime Minister Tony Abbott has refused to address claims thatof Indonesian President, Susilo Bambang Yudhoyono, in 2009.
Responding in parliamentary Question Time today, Abbott said that all governments gather information and all government know that every other government gathers information, but that he would not be drawn on commenting on this alleged incident.
"Australian government never comments on specific intelligence matters, this has been the long tradition of governments of both political persuasions, and I don't intend to change that today," he said.
"I should also say that the Australian government uses all the resources at its disposal, including information, to help our friends and our allies, not to harm them."
Abbott said that his first duty was to protect Australian and advance its national interest, and that he would never depart from that duty.
"Consistent with that duty, I will never say or do anything that might damage the strong relationship and the close co-operation that we have with Indonesia. Which is, all in all, our most important relationship, a relationship that I am determined to foster, a relationship that I am determined will grow stronger in the months and years ahead."
In response to the allegations, a spokesperson for the Indonesian president told the ABC that the Australian government urgently needed to clarify the issue, in order to avoid further damage.
"The damage has been done," the spokesperson said.
Senator Scott Ludlam of the Australian Greens said full disclosure was needed on what Australian spy agencies were up to, and covert surveillance had hit a tipping point.
"The Greens believe there must be an immediate inquiry into surveillance overreach and the damage it is doing to diplomacy, business confidence and personal privacy protections. Last week the Government and Labor party voted down a resolution to this effect; the Greens intend to give them another opportunity soon," he said in a statement.
"Are we seriously meant to believe that the President of Indonesia, his wife and his leadership team are a national security threat to Australia?"
"The Government cannot continue to pretend this isn't happening."
Former coalition government foreign minister Alexander Downer says the revelations are damaging to Australia.
"It's a shocking situation in which Australia will pay a big price," Sky News cited Mr Downer as saying.
Richard Woolcott, a former Australian ambassador to Indonesia, agreed the latest revelations about spying might ratchet up the reaction from Indonesia, but played down speculation of a possible recall of the Indonesian ambassador.
"When you have problems, the best thing to do is keep your ambassador there," he said.
Tasmanian federal independent MP Andrew Wilkie said he supported Edward Snowden's actions in releasing the sensitive material revealing attempts to tap the Indonesian president's mobile calls.
"I have no doubt he acted in the public interest when he revealed the information," he told reporters in Canberra. "Good on him."
Wilkie said it was important that "we all know how our intelligence services operate".
"Some capabilities must be kept secret ... but it is in the public interest that a light be shone on the way these agencies do business and how they spend billions of dollars of our money."
Wilkie is a former intelligence analyst who resigned his job with the Office of National Assessments in 2003 due to concerns over Australia's involvement in the invasion of Iraq.
Earlier on Monday, the ABC and The Guardian quoted a top-secret document from US National Security Agency whistleblower Edward Snowden that lists the senior Indonesian officials targeted by Australia. The document, dated November 2009, is shown on the ABC website and has an Australian Department of Defence letterhead. The headline is "IA Leadership Targets + Handsets".
The president is top of the list and his wife, Kristiani Herawati, better known as Ani, is second. Vice-President Boediono, who visited Australia last week, is third and his predecessor Jusuf Kalla is fourth.
Others in the top 10 include former presidential spokesmen Dino Patti Djalal and Andi Mallarangeng.
Former finance minister Sri Mulyani, now a managing director at the World Bank, is also listed.