Myuran Sukumaran, 34, was executed by firing squad with another Australian, Andrew Chan, and five other foreign drug convicts last week, sparking a storm of international condemnation.
Australia withdrew its ambassador to Jakarta in protest at what it called the "cruel and unnecessary" executions of the pair, who were ringleaders in a plot to smuggle heroin out of Indonesia.
Despite the global outrage, President Joko Widodo has stayed firm in his support for the death penalty, insisting that Indonesia is facing an emergency due to rising narcotics use.
"I just asked you not to order his death but instead you ignored me and many others," she wrote.
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"I asked to meet you, to speak to you but once again you could not even have the courage to face our requests to communicate with you."
She said that in recent months she had watched Widodo "openly discussing the way in which he would die, parading and humiliating our family".
"Think for a second, one of your children is tied to post, and men are lined up in front of them and the fear he would have felt, and then your child is shot through the heart," she added.
Raji Sukumaran finished the letter saying she would pray "for the many other men and women whose lives are in your hands, especially those on death row.
"I pray that you will have the courage to look beyond the politics for they too have families who love them despite their mistakes."
While the executions have cast a shadow over the often tense relationship between Jakarta and Canberra, Australian Prime Minister Tony Abbott has said he is confident ties will be restored.