Labor defence spokesman Robert McClelland will put forward a motion calling on Indonesia to "understand" Australia's opposition to the death penalty after receiving the moving letter.
Fairfax newspapers report that Rush wrote the letter to Mr McClelland after his appeal against the death penalty was rejected by Indonesia's Supreme Court last month.
In the letter, he apologises unreservedly for all the pain he has caused and calls for a "just penalty" and sentence.
"I have learnt so much in the time I have been here, and in the time that I have had to face my future with my faith and final courage," he wrote.
Mr McClelland said he would now put forward a private member's notice of motion calling on Indonesian President Susilo Bambang Yudhoyono to extend clemency.
It will also call on Dr Yudhoyono to commute the sentences if a challenge to the execution fails and to "note and understand Australia's strong opposition to the death penalty".
Mr McClelland said the motion will not mention the Australian Federal Police's decision to allow Rush to leave Australia for Bali even though his father tipped them off about the trip.
But, MPs could express their feeling on this issue if the motion was debated, Mr McClelland said.