He said the men would prefer to be beheaded.
Mahendradatta also complained that the sentence would be an act of "murder" as the courts had not followed due legal process by refusing to allow them to appear in person during their previous appeals.
"This is a criminal case that obliges the court to hear the defendant," he said.
However, Bonaventura Daulat Nainggolan, a spokesman for the Indonesian attorney-general's office, said that the new legal bid would not delay the execution.
"As long as there is no decision by the constitutional court, then the law has legitimacy," he said.
The three men lost their final appeal early this month and the attorney-general's office said it holds documents from the families and the bombers that waive their legal right to ask for a presidential pardon.
Amrozi, Mukhlas, and Imam Samudra were convicted over their roles in organising and carrying out the co-ordinated bombings of nightclubs on the resort island of Bali in 2002 which killed 202 people, mainly foreign tourists.