Indonesia's foreign minister says he understands Australia has promised to stop tapping the phones of the Indonesian leadership but has not agreed to completely stop gathering intelligence in the country.

Australia targeted Indonesian president Susilo Bambang Yudhoyono, his wife, and senior ministers in a phone-tapping operation in 2009.

Prime Minister Tony Abbott wrote to Mr Yudhoyono after the incident came to light, telling him Australia would not do anything in the future that would hurt Indonesia.

But Mr Abbott told Fairfax Radio today that Australia will not stop collecting intelligence in Indonesia.

"No, [we will not stop collecting intelligence on Indonesia] and they [Indonesia] certainly haven't agreed to stop collecting intelligence on Australia," he told Radio 3AW.

"But we are close friends. We are strategic partners. I certainly want Australia to be a trusted partner of Indonesia and I hope Indonesia can be a trusted partner of Australia."

Indonesia's foreign minister Marty Natalegawa says he does not have a problem with Mr Abbott's comments.

"I don't see anything inherently inconsistent with that kind of statement," he said.

"The collection of intelligence and information is something that countries do, but it must be done under a cooperative framework.

"If all this is being done as part of the formal, inter-agencies, inter-intelligence agencies framework, I think that is very much consistent with the spirit and the letter of the kind of approach that we are promoting just now."

Mr Natalegawa says it is understood that Mr Abbott has promised to stop the type of spying used on Mr Yudhoyono in 2009.

Foreign Minister Julie Bishop met with her Indonesian counterpart yesterday, the first step in mending bilateral relations.

The two countries have agreed to set up a hotline between Canberra and Jakarta to avoid any misunderstandings.

Mr Natalegawa says Indonesia wants to move on.

"You can talk about the details, about who's doing what and all that, but in the final analysis we have to rebuild that trust and I believe that process of rebuilding trust is now very much underway," he said.

"Indonesia, both the government and the people of Indonesia, has the huge reservoir of goodwill for Australia and we have a real interest in wanting to move forward."