The Israeli military said it was investigating after reports emerged four foreign aid workers had been killed in Gaza.
Israel's top diplomat in Australia has been requested for a call-in by the Department of Foreign Affairs and Trade over the death.
"We want full accountability for this, this is a tragedy that should never have occurred," Mr Albanese told reporters in Queensland on Tuesday.
Anthony Albanese says Israel's top diplomat in Australia has been summonsed over the death. (Darren England/AAP PHOTOS)
The department was "urgently" investigating the incident, he added.
Ms Frankcom's social media pages say she worked for World Central Kitchen, a charity founded by chef Jose Andres, which delivers meals to people displaced during humanitarian emergencies.
World Central Kitchen board member Robert Egger wrote in a Facebook post: "Sending love, sorrow and solidarity to my brothers and sisters at World Central Kitchen.
"Viva Dear, Caring Zomi Frankcom and her courageous colleagues."
Photos posted on social media show the woman's bloodied body with an Australian passport placed on her chest.
She has been described by loved ones on social media as a "dear friend" who had "risked her life many times to help those in dire need".
"Rest in peace our beautiful sister… xox," a friend wrote.
Mr Albanese said his government has supported a "sustainable ceasefire".
"I'm very concerned about the loss of life that is occurring in Gaza," he told ABC radio.
"We've called for the release of hostages and there have been far too many innocent lives, Palestinian and Israeli, lost during the Gaza-Hamas conflict."
We are aware of reports that members of the World Central Kitchen team have been killed in an IDF attack while working to support our humanitarian food delivery efforts in Gaza. This is a tragedy. Humanitarian aid workers and civilians should NEVER be a target. EVER.— World Central Kitchen (@WCKitchen) April 1, 2024
The other dead aid workers were placed alongside the Australian woman and were pictured with British and Polish passports.
The nationality of the fourth aid worker is not yet known.
The Israel Defense Forces says it is conducting a "thorough review at the highest levels to understand the circumstances of this tragic incident".
"The IDF makes extensive efforts to enable the safe delivery of humanitarian aid, and has been working closely with WCK (World Central Kitchen) in their vital efforts to provide food and humanitarian aid to the people of Gaza," it said in a statement.
Posting to X, formerly Twitter, World Central Kitchen responded to the news of the deaths.
"This is a tragedy," they wrote.
"Humanitarian aid workers and civilians should NEVER be a target. EVER."
The Australian Council for International Development said it expressed its deepest condolences to the family of Ms Frankcom.
"It is truly tragic that an Australian aid worker, working to provide food to starving civilians, has been killed in this fashion," chief executive Marc Purcell said.
