The executions of convicted Australian drug smugglers Andrew Chan and Myuran Sukumaran have sparked an "unprecedented" diplomatic response, with Australia withdrawing its ambassador from Indonesia in protest.

Mr Abbott confirmed the move to withdraw ambassador Paul Grigson this morning, saying Australia deeply regretted the "cruel" and "unnecessary" executions and acknowledging it was a "dark moment" in the relationship between Australia and Indonesia.

"We do deplore what's been done and this cannot be simply business as usual," he said.

"For that reason, once all the courtesies have been extended to the Chan and Sukumaran families, our ambassador will be withdrawn for consultations.

"I want to stress that this is a very important relationship between Australia and Indonesia but it has suffered as a result of what's been done over the last few hours."

Australia has not previously taken this step when a citizen has been executed by a foreign country, and it has never before withdrawn an ambassador to Indonesia.

"It is very unusual, indeed unprecedented, for an ambassador to be withdrawn so I don't want to minimise the gravity of what we've done," Mr Abbott said.

"Ministerial contacts have been suspended for some time. Once it became apparent that the executions were likely, ministerial contacts were suspended, and they will remain suspended for a period."

But Indonesia's attorney-general Muhammad Prasetyo has dismissed the withdrawal as a "temporary reaction".

Mr Prasetyo, who was in charge of the executions, said the Netherlands and Brazil took the same measure after their citizens were executed in January.

Foreign Minister Julie Bishop said Mr Grigson would return by the end of the week to discuss "the way forward" in Australia and Indonesia's relationship.

"The withdrawal of an ambassador is to register our displeasure at the way our citizens have been treated," Ms Bishop said.

Standing beside Mr Abbott at this morning's press conference, Ms Bishop confirmed the two men's deaths, and said she had been notified that gunfire had been heard from the jail during the night.

"It is with a very heavy heart that I confirm, despite our ongoing efforts right up until the last minute, to seek a stay of execution, our Australian citizens Mr Andrew Chan and Mr Myuran Sukumaran were put to death early this morning," she said.

Ms Bishop said Australia's consul-general was on the prison island to formally identify the two men's bodies but she was yet to hear from her.

"She's not entitled to have a telephone at the prison but we must assume that the executions have taken place and that she is in the process of formally identifying the bodies," Ms Bishop said.

"We have not yet received formal identification from the Indonesian Government that the executions have taken place but we can assume that they have."

Ms Bishop said the men's bodies would be brought back to Australia for burial.

Opposition supports ambassador withdrawal

The Government's response has received widespread support but Opposition Leader Bill Shorten has suggested further action could be taken.

"We are disgusted at the futile act of execution of these two young Australian men," he said.

"I contacted the Prime Minister Tony Abbott on Sunday and we had a discussion about potential options.

"We will talk with the Government in coming days about other responses."

Opposition foreign affairs spokeswoman Tanya Plibersek described the Indonesian government's handling of the case as "chaotic and insensitive".

"The treatment of the families of these young men and the refusal of the Indonesian Government to deal fairly with the Australian Government, in terms of informing them this morning [that the executions had taken place] ... has been quite reprehensible," Ms Plibersek said.

Both Mr Abbott and Ms Bishop expressed frustration that Australia's "strenuous" representations on behalf of the two men had been "in no way heeded" by Indonesia.

Mr Abbott described the executions as an "appalling tragedy" for the two men's families.

"[The executions are] cruel because both Andrew Chan and Myuran Sukumaran spent some decade in jail before being executed and unnecessary because both of these young Australians were fully rehabilitated while in prison," he said.

When asked whether Australia would consider cutting the $600 million in aid it gives to Indonesia each year, Ms Bishop said any announcement would be made at budget time in May.

"Now is a time to be thinking of the Chan and Sukumaran families to spare a thought for what they are going through today and to provide them with all the support and assistance that we can," she said.

"It's an appalling situation for them. Anyone who saw the film footage of what they had to go through yesterday, it was a ghastly episode and I think today is the time to focus on supporting the families and providing them with assistance."

Calls for further investigations

Greens Leader Christine Milne said it was important for Australia to take a strong stand and called for an international inquiry into Indonesia's judicial system.

"In particular, the interference or the apparent interference in the sentencing and the judicial system that went on," she said.

"That is in front of the constitutional commission in Indonesia at the moment but I think the international community needs to look into how that happened and whether or not the attorney-general in Indonesia was specifically involved in that decision to direct the judges to find in terms of coming down with the death penalty."

Independent Senator Nick Xenophon, who travelled to Indonesia last month to add his voice to pleas for clemency, has described Indonesian president Joko Widodo as a "pathetically weak leader".

And he said serious questions remained about the level of cooperation between the AFP and Indonesian authorities in the arrest of the Bali Nine drug smugglers.

"I will be writing this morning to the joint standing committee on Foreign Affairs of the parliament to ask that this matter be looked at. It is legitimate to do so," Senator Xenophon said.

"This is not about recriminations, it is about making sure that this never, ever happens again."

Independent MP Clive Palmer also wants to tackle the question of AFP involvement through new laws that would ban Australian public officials from disclosing any information that could lead to Australians facing the death penalty.

"We can't do much for the people that have lost their lives or their families but we can ensure that they are like a beacon of hope for those who go after them to ensure this doesn't happen again and Australian public servants or officers we employ with taxpayer' money do carry out their duties in the best interests of Australians," he said.