A survey by the Sydney-based Lowy Institute think tank showed strong public disapproval of the executions, with 62 percent of the 1,211 people surveyed opposing the move. A social media campaign is urging Australians to boycott Bali, a popular destination.
However, one business executive in Australia criticized the government's support for the pair, saying it had soured ties with Indonesia.
"Some of the public statements made by our most senior politicians demonstrate that they have a very naive understanding of the importance of Indonesia to Australia," Peter Lynch, chairman and CEO of coal miner Cokal told Reuters.
Cokal, which is developing a coal project in Kalimantan on Indonesia's side of Borneo island, on Tuesday received a takeover offer worth at least $54 million from Indonesian firm Cakra Mineral.
Legal appeal outstanding
Putra Surya Atmaja, head of the provincial prison division in Bali, told reporters Sukumaran and Chan were being transferred after having "plenty of chances and time with the family".
The pair have made numerous appeals against their death penalty sentence. One of those, which challenges Widodo's refusal of clemency, is still outstanding.
Peter Morrissey, a Melbourne-based lawyer for the men, said it would be a breach of the rule of law if the executions went ahead before that was resolved.
Asked before the early-morning transfer if the pair were prepared for execution, Morrissey said: "They're coming to terms with that ... it's a very raw time for them."
Abbott said Australia's lobbying on their behalf had shown some promise, but he no longer wanted to hold out false hope.
"There were some suggestions earlier that perhaps at least some people in the Indonesian systems were having second thoughts but I'm afraid those signals seem to be dissipating," he said.