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 Radio National on Friday.
"And the aspect of reparations can be checked, definitely."
But Dr Newman said a request needed to be made before Israel could investigate potential reparations.
Amnesty International Australia's Occupied Palestinian Territory spokesperson Mohamed Duar said reparations could include an official public apology, compensation, restitution and memorialisation.Â
"Australia should immediately introduce a two-way arms embargo. Use all diplomatic and economic ties that fuel this genocide, occupation, and apartheid," he told AAP.
Prime Minister Anthony Albanese labelled Israel's response to the attack as a "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.
Ms Frankcom's family said the findings were a miscarriage of justice and an insult to her legacy.
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.
Foreign Minister Penny Wong on Thursday condemned the actions of Israel, saying they fell short of the accountability Australia expected.
A spokeswoman for the 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.
Australian Council for International Development chief executive Matthew Maury said the government should support all credible international accountability measures including pushing for an International Criminal Court investigation.
"We need to ensure there is an independent examination of the circumstances surrounding the deaths of Zomi Frankcom and her World Central Kitchen colleagues and that true justice can prevail," he told AAP.
Greens foreign affairs spokesman David Shoebridge said Labor needed to take further action against Israel.
"This is about responding to another country murdering an Australian citizen and then refusing to do anything about it," he told reporters in Canberra.
"What we need is our government to respond to that murder by putting in place sanctions against the Israeli state, ending the two-way arms trade, and cancel the multi-billion dollar contracts with Israeli arms manufacturers."
Pro-Palestinian advocates in addition to the Jewish Council of Australia, have demanded sanctions be placed on Israel.
