Andrew Chan and Myuran Sukumaran, the ringleaders of the so-called "Bali Nine" drug trafficking gang, were moved on Wednesday to the island where they are due to be killed.
Australia was dismayed at the level of security used to transport them from Bali to the so-called "execution island" of Nusakambangan, with dozens of armed police on hand, and outraged that photographs emerged from on board the plane.
Another showed the commissioner placing his hand on the shoulder of Sukumaran, who was looking up at him.
"I thought they were unbecoming and showed a lack of respect and dignity and we have protested to the Indonesian ambassador here in Canberra," Abbott told reporters of the pictures that were widely published in Australia.
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Treasurer Joe Hockey added that the treatment of the pair had been inappropriate.
"It was incredibly insensitive, it's almost macabre the way this has been handled by the Indonesian authorities," he said.
Australia on Thursday proposed a prisoner swap in an 11th-hour bid to save them, but it was rejected by Jakarta which said the men had "poisoned our nation".
Chan and Sukumaran are among a group of drug convicts, including foreigners from France, Brazil, the Philippines, Nigeria and Ghana, who are expected to be executed at the same time on the prison island.
Authorities must give them 72 hours' notice before they are shot dead and reports on Friday suggested their executions could be pushed back by up to 10 days.
"About notification, it's a minimum three days before the execution," he said. "It could be 10 days."
Fairfax said the delays were believed to be related to legal appeals, not only for the Australians but also Frenchman Serge Atlaoui and Filipina Mary Jane Fiesta Veloso.
As well as Australia, Brazil and France have piled pressure on Jakarta, with Paris summoning Indonesia's envoy and the Brazilian president refusing to accept the credentials of the new Indonesian ambassador.