Israel struck the capital Doha on Tuesday targeting the leadership of Hamas, which Australia designates a terror group, and said five of the group's members were killed.
The strike has sparked widespread criticism from allies including the US and the UK.
Qatar has helped mediate peace talks between Israel and Hamas during the war in Gaza and condemned the attack as a "criminal assault" and "blatant violation of all international laws and norms".
Speaking from Honiara, the prime minister pointed to the US position of Qatar's sovereignty being violated.
"It risks the ceasefire," Mr Albanese said on Wednesday.
"I want to see peace in that region, I don't want to see an escalation."
Acting Prime Minister Richard Marles reaffirmed Australia's view of Israel's strikes.
"They risk a ceasefire in Gaza, they do not help in terms of a return of the hostages and they also risk an escalation in what's occurring in the Middle East," he told reporters in Sydney.
"For all those reasons, we are deeply concerned about Israel's strikes on Qatar."
Israel has taken full responsibility for the attack, but the strike has angered many of its international allies.
Foreign Minister Penny Wong said Qatar had been playing a crucial role in the region.
"We don't think it was the right thing to do," she told Seven's Sunrise program.
"They've been tireless in those negotiations, that's the context in which this strike has occurred."
US President Donald Trump said the strike "does not advance Israel or America's goals," while UK Prime Minister Sir Keir Starmer condemned Israel's actions.
Qatari leaders have said they remain committed to brokering a ceasefire agreement despite the attacks.
Australia was not given any specific information by Israel about the attacks before they took place, while the US was given a heads-up.
Australia/Israel and Jewish Affairs Council executive director Colin Rubenstein said the strike targeted the most senior Hamas leadership who were "directly responsible for the brutal October 7 massacre".
"It should also be remembered that Qatar itself is far from an innocent bystander or neutral 'mediator'," he said.
"They are one of Hamas' most important allies, hosting its leadership in lavish style, supplying the terror groups with funds."
Israel's action demonstrated its government was not serious about having hostages returned, Greens foreign affairs spokesman David Shoebridge said.
"This latest gross breach of international law proves Israel does not want a negotiated ceasefire and that the US will continue to enable their lawless violence," he said.
Hamas, which controls Gaza, invaded Israel's south in October 2023 and killed more than 1200 Israelis while taking about 250 more hostage, with some still being held.
Almost 63,000 Palestinians in Gaza have been killed by Israel's military response and many more face starvation in the war zone.
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