Andrew Chan, 31, and Myuran Sukumaran, 34, were executed by firing squad on Wednesday over their role in a plot to bring heroin to Australia from the Indonesian resort island of Bali, despite international pleas to Jakarta for clemency.

Abbott said he understood the dismay and anger over the executions but respected Indonesia's sovereignty.

"It really was terrible that these cruel and unnecessary executions went ahead," he told reporters in Sydney.

"Our anger and our grief, sadly, is not going to bring those two young men back.

"The important thing now is not to do any thing that would make a difficult situation worse."

The Department of Foreign Affairs and Trade was unable to confirm reports that the men's bodies were on a flight which touched down early Saturday in Sydney.

The flight was carrying Sukumaran's parents, brother and sister and Chan's wife Febyanti Herewila, who married him on the eve of his execution.

The Australian Broadcasting Corporation said Chan's mother and brother were understood to have wanted to travel back with his body, but were unable to due to a hold-up with the repatriation. They returned on Friday.

Chan and Sukumaran were among seven foreigners and one Indonesian executed in Indonesia in the early hours of Wednesday.

The Australians had spent a decade in prison for their role in masterminding the so-called 'Bali Nine' group of smugglers, during which time Chan had become a Christian pastor and Sukumaran had studied art.

The executions have cast a shadow over Australia's relationship with its important neighbour Indonesia, with Abbott withdrawing Canberra's ambassador to Indonesia.

But the prime minister said Saturday that it remained important for the country's future that the relationship with Jakarta be restored.

"I am confident that we will be able to rebuild the relationship," Abbott said.

"It's important to Australia, it's important to Indonesia and it's important to the wider world that Australia and Indonesia's friendship is strong and growing in the months and years ahead."

Australia and Indonesia are key allies in counter-terrorism efforts, while Indonesia is also a significant economic partner.

Earlier, Abbott had he described as "odd" a decision by the Australian Catholic University (ACU) to introduce scholarships in memory of the executed pair for Indonesian students wishing to study in Australia.

"We did this because ACU is committed to the dignity of the human person, and that applies equally to all human beings: victims as well as to those who have been convicted of crimes," Vice Chancellor Greg Craven said.

Abbott said the men had met their deaths with a "kind of nobility", but he questioned whether that justified establishing scholarships in their name.

"I know part of Christian faith is forgiveness, but another part of Christian faith is calling people to be their best selves," he told commercial radio late Friday. (++++)

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