As a result of Australia's alleged spying on Indonesian President Susilo Bambang Yudhoyono's phone activities - including Australia's target phone tapping of his wife and top Indonesian officials - Indonesian social media sites are now reeking with anti-Australian comments.

Hence, Foreign Minister Julie Bishop expressed that Australia is taking the spy concerns on Indonesia as an "exceedingly serious" matter. However, she did not give the specifics of the government's plan of action.

On Monday, Indonesia summoned up its ambassador to Australia saying that the revealed spying activities threatened the relationship between Indonesia and Australia. In fact, Indonesia threatened that it might expel Australian diplomats from its capital.

Indonesia demanded a complete account of the spying activity to be made public. The country also demanded a pact with Australia vowing not to engage in any spying activities again.

Foreign Minister Marty Natalegawa told reporters that he personally condemns Australia for its betrayal.

"This is an unfriendly, unbecoming act between strategic partners. This isn't a smart thing to do. It is, I want to make it absolutely clear, an unfriendly act unbecoming of relations between strategic partners... It violates every single decent and legal instrument I can think of; national in Indonesia, national in Australia, international as well. It is nothing less than an unfriendly act which is already having a very serious impact on bilateral relations," Mr Natalegawa said during a press conference.

Special adviser for political affairs Daniel Sparringa said that the spying activities devastated Indonesia as President Yudhoyono had always been giving special attention to the country's relationship with Australia.

President Yudhoyono's foreign affairs spokesman Teuku Faizasyah laments that "damage has been done and now trust must be rebuilt."

Meanwhile, Prime Minister Tony Abbott was elusive about whether Australia will make an apology. Instead, he said that "today may not be the best day" to discuss the relationship between Indonesia and Australia.

"It's in no one's interests to do anything or to say anything that would jeopardise that relationship, and certainly I'm not going to," Mr Abbott told AAP.

He still insists that Australia's relationship with Indonesia is as good and strong as before.