Indonesia believes that Australia has signed up to a “no further espionage” future, while Prime Minister Tony Abbott is adamant that Australia will continue to collect intelligence on its neighbour.

Indonesian foreign minister Marty Natalegawa said he took Julie Bishop's commitment on Thursday not to use its intelligence-gathering apparatus to harm Indonesia as a “very important commitment” to stop entirely the “extraterritorial, unlawful type of intelligence or information gathering, data collection”.

He acknowledged that countries collect intelligence on each other, but “it must be done under a co-operative arrangement”.

“If all this is being done as part of the formal, inter-intelligence agency framework, I think that's very much consistent with the spirit and the letter of the kind of approach we are advocating just now,” he told ABC News 24 on Friday.

In a later interview with Fairfax Media, he said the “most and important element” of the mooted intelligence-gathering code of conduct between the two countries was “No spying. No more bugging. No more tapping.”

When Mr Abbott was asked on Fairfax Radio if Australia had agreed to stop collecting intelligence on Indonesia, he said: “No. And they certainly haven't agreed to stop collecting intelligence on Australia”.

“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.”

However, Mr Abbott chided Indonesia over its temporary withdrawal of joint support for people smuggling operations during the current dispute, saying: “I do expect continued co-operation from Indonesia” to combat people smuggling.

“The point I've been making as politely as I can to the Indonesians is that as far as we're concerned this is a sovereignty issue”.

He drew an apparent link with a pair of small protest vessels, the Freedom Flotilla, which intended shortly after the Australian election to carry a group of West Papua protesters from Australia to the controversial Indonesian territory.

“When a couple of West Papuan boats were planning to proceed from Australia to Indonesia, very rightly, the Indonesians said, well we want you to do everything you can do to stop them and we did, and we did,” Mr Abbott said.

Asked about those comments, Mr Natalegawa said: “I think this is not directly linked and I don't think we should be in the business of linking one issue with the other.”

Mr Natalegawa said that president Susilo Bambang Yudhoyono had been pleased with reports of the meeting with Ms Bishop, but that it was “just the first step towards the normalisation of the Indonesia-Australia relationship and the road is still long, and even winding”.

He did not confirm if the two countries could now move to the second stage of the president's six-step plan — negotiating a spying “code of conduct”.

“This is a process. I think it will not be solved overnight, but yesterday's meeting was definitely very helpful because we discussed sensitive issues openly and very deeply.”