Ms Frankcom's aid convoy was targeted by air strikes in April 2024 while working with colleagues to deliver food and basic supplies in the Gaza Strip.
The Israeli military on Thursday announced it had found there was no suspicion of criminal misconduct surrounding the Australian's death, despite a previous finding there had been failures in how it was carried out.
Israeli ambassador Hillel Newman was summoned to Parliament House on Thursday morning to explain the outcome of the two-year investigation.
"Israel is open to discussions of a legal aspect, we can share information with legal teams of Australia," he told ABC's RN on Friday.
"And the aspect of reparations can be checked definitely."
Dr Newman said a request needed to be made before Israel could investigate potential reparations.
Prime Minister Anthony Albanese labelled Israel's response to the attack as a "so-called" and "nothing to see here" report.
"Australia deserves better," he told ABC's 7.30 program.
"There's a need for a far more transparent and clear explanation from the Israeli government."
Mr Albanese said he would work with Ms Frankcom's family to call for an independent review into the attack.
"We will press the Israeli government. The direction, we have said today, we'll discuss with Ms Frankcom's family," he said.
"They deserve to be consulted on these issues, and we'll do that, and then we'll make an announcement in the coming days."
Ms Frankcom's family said the findings were a miscarriage of justice and an insult to her legacy.Â
Israel has also refused to release audio from the drone strikes that targeted the aid convoy.
"Zomi and her colleagues deserve more than an internal, opaque process that ends with a short statement by the Israeli military absolving their soldiers of criminal wrongdoing," Ms Frankcom's family said in a statement.
Penny Wong on Thursday condemned the actions of Israel, saying they fell short of the accountability Australia expected.
A spokeswoman for the foreign affairs minister said she spoke with her Israeli counterpart Gideon Sa'ar later that night.
"The minister conveyed Australia's view and expectations as she did with the Israeli ambassador," the statement released on Friday reads.
Calls grew throughout the day for Dr Newman to be expelled from Australia over his refusal to apologise for Ms Frankcom's death.
Pro-Palestine advocates, including Greens Senator Mehreen Faruqi and the Jewish Council of Australia, also demanded sanctions be placed on Israel.
"Penny Wong says this decision falls short of the accountability we expect. She's right. So why is the response to a complete failure of accountability just a stern word to the ambassador," the Jewish Council's executive director Sarah Schwartz said in a statement.
Senator Wong maintained that ties with Israel were important for advancing Australia's diplomatic interests.
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