Labor deputy Tanya Plibersek has criticised the Prime Minister's handling of relations with Indonesia after the fallout from revelations of Australian spying.

Speaking to the ABC's Insiders program, Ms Plibersek pointed to several "mis-steps" in Mr Abbott's efforts to deal with the crisis, which was sparked by news that Australian spies tapped the phones of Indonesian president Susilo Bambang Yudhoyono and his inner circle, including his wife.

An angry Mr Yudhoyono last week said all military and intelligence cooperation with Australia was on hold until he received a proper explanation.

Mr Abbott, who says one of his priorities as Prime Minister is to maintain a strong relationship with Indonesia, wrote a letter to Mr Yudhoyono about the affair, which on Sunday afternoon the Indonesian leader was said to be examining.

The Government has kept the contents of the letter to itself, but Ms Plibersek says it should "assure the Indonesian president that we are friends of Indonesia and that we are keen to re-establish normal relationships as quickly as possible".

"We need to see whether they re-establish normal relationships," she said.

"We've seen a number of areas of cooperation under stress or suspended. I think the proof will obviously be in the pudding, if that cooperation's restored to its normal settings then we will know that the letter has been successful."

However, the Deputy Opposition Leader believes Mr Abbott has not handled the fallout from the revelations well.

"I don't know that it has been a terrific performance when it comes to handling the diplomatic crisis," she said.

"There were, I suppose, a few mis-steps before this and then I think the two occasions when the PM's addressed the Parliament were really a long way from helping settle things down.

"I don't think really what he said to the Parliament has settled things down at all."

Labor's role in spying 'separate' to diplomatic row

Opposition Leader Bill Shorten has advocated a "Team Australia" approach to diplomacy over the crisis, saying it is not a "Liberal or Labor issue."

He said on Sunday the issue is above political point-scoring and he would not give Mr Abbott advice on diplomacy through the media.

"Now is the time for cool heads and careful words. We cannot disguise the fact that our Indonesian friends have been offended - we've got to recognise that," he said.

"I think all Australians are disturbed with what's happened over the last few weeks with the [Australia-Indonesia relationship] and want to see things get back on track.

"That's what people expect their members of parliament to do when you've got these difficult situations - to see some mature experience, not simple political point-scoring."

Sorry, this video has expired Bill Shorten discusses Indonesian spying row

Ms Plibersek earlier sought to distance Labor's role in the affair, saying that whether or not the spying occurred under Kevin Rudd when he was prime minister was a "separate thing" to diplomatic relations between Australia and Indonesia.

"The diplomatic relationship, how we get on, is not determined by this one event or any particular event, it's about trust and open communication and relationships at all levels of government over a number of years," she said.

"I'm sure that we will get the relationship back on track, but we need to do it quickly and that's why, I guess, so much is hanging on this letter that the PM has sent to the Indonesian president."

Ms Plibersek suggested the rift with Indonesia had been exacerbated by the Coalition's policy statements in the lead-up to the election, and Mr Abbott had done little since to repair any damage.

"I think certainly the Indonesians were very disappointed to hear during the election campaign the Coalition talking about stopping the boats, buying back the boats, turning back the boats, things that were - policies that were to take place on Indonesian soil or in Indonesian waters without having ever discussed that with the Indonesians," she said.

"And then of course when the PM was in Indonesia locking the Indonesian press out of his press conference, I don't think [that] has disposed the Indonesian media to be particularly interested in settling things down now either.

"The thing about a relationship between two countries is it's never one event that makes things go smoothly or diverts things from a smooth path.

"It's a relationship over very many years, and over very many years both sides of politics have sought to improve our relationship with Indonesia.

"From the 1940s onwards we've had a very good relationship that's built over time, certainly I give [former Liberal prime minister John] Howard great credit for the swift way that he responded to the tsunami and the billion-dollar contribution then certainly was a great thing for our relationship with Indonesia, just as [former Labor prime minister] Paul Keating's visits there in the '90s were very important for establishing a strong diplomatic relationship.

"Each government has done its best to improve and strengthen the relationship.

"I think we need to get back onto that track of growing friendship and growing trust as quickly as we can."

Indonesia reaction fostering 'negative attitudes': Downer

Meanwhile, Australia's longest-serving foreign minister Alexander Downer says he believes Indonesia's reaction to the spying scandal is generating negative attitudes among Australians towards Indonesia.

"I think initially Australians thought, 'whoops, it looks like we've done something wrong here'," Mr Downer told Sky News.

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"But the reaction from Indonesia has ramped up day by day, and a lot of the rhetoric has been very fiery rhetoric and that's made Australians recoil a little bit."

Mr Downer suggested setting up an intelligence code of conduct with Indonesia.

Ms Plibersek told Insiders unhelpful comments had been made on both sides of the dispute.

"I think if you look at what's happening in both Australia and Indonesia at the moment, you see people engaging in the public debate that are not interested in settling things down or sorting things out," she said.

"We've seen commentary in Australia, we've seen commentary in Indonesia that's not helpful when it comes to restoring the relationship. I don't agree with those sentiments."