"The prime minister (Tony Abbott) has written again to President (Joko) Widodo," Bishop said.
"The Australian government will continue to make representations at the highest level."
Brazil and the Netherlands recalled their ambassadors from Indonesia and expressed fury yesterday after Jakarta put to death two of their citizens along with four other drug offenders from Vietnam, Malawi, Nigeria and Indonesia.
The six were the first people executed under new President Widodo, who took office in October and has voiced strong support for capital punishment.
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One of the pair, Myuran Sukumaran, had his clemency appeal rejected last month but authorities say he will be executed with fellow Australian Andrew Chan as they committed their crime together.
Chan is still awaiting the outcome of his clemency appeal.
Bishop skirted round questions of Australia withdrawing diplomats from Jakarta, noting they were required to stay to plead with the government.
She said the foreign ministry had recently replied to her own letter "rejecting our representations on the basis that Indonesia claims it is facing a crisis in terms of drug trafficking and it believes that the death penalty should apply."
"I don't believe executing people is the answer to solving the drug problem.
"However, this is Indonesian law and it is a sober reminder that drug related offences carry very, very heavy penalties in other countries, particularly in Indonesia."
Widodo pledged in December there would be no pardons for drug traffickers on death row, including foreigners.