Mr Albanese told the ABC that Australia has maintained "a bipartisan position of opposition to the death penalty" and that the government was seeking advice on its options, while acknowledging that blocking the broadcast was not as simple as "turning off a light switch."
"We should do whatever we can to stop that occurring," he said.
US Defence Secretary Pete Hegseth said last week that Hasan's execution would be available for the public to watch, though Vice-President JD Vance has cast doubt on that plan. President Donald Trump has indicated he is weighing the matter, and Mr Albanese said he hoped "there is a response in the United States as well."
The eSafety Commissioner said on Monday it could not prevent Australians from seeing the execution. "While eSafety does not have powers to proactively prevent a live stream from occurring online, online services have responsibilities under Australia's online safety regulatory framework to protect users from harmful material," a spokesperson said.
Mr Albanese said he would make it "very clear" to social media platforms that the content had no place in Australia. "I think anybody broadcasting this will damage their own reputations as well. They have a social responsibility here to do the right thing," he said. The ABC has contacted Google, Meta and TikTok but has not received responses.
The proposal has drawn concern across the political divide in parliament. Greens Leader David Shoebridge asked Foreign Minister Penny Wong about the "shared values" between Australia and "a government that publicly broadcasts state-sanctioned snuff films." Senator Wong said it would be "deeply distressing for any such vision to be live streamed," adding: "We don't believe anyone should be confronted with it, particularly younger Australians."