The temporary pause in hostilities between Israel and Iran was announced by US President Donald Trump on Tuesday after almost two weeks of conflict.
"What we want to see is the ceasefire announced by President Trump implemented," Mr Albanese told Sky News on Tuesday.
"We do want to see dialogue and diplomacy replace any escalation and President Trump's announcement we very much welcome."
The prime minister has faced criticism from the federal opposition that he was too slow to respond to US military strikes on Iranian nuclear facilities.
Mr Albanese did not make public statements backing the US involvement until more than 24 hours after they took place.
Opposition home affairs spokesman Andrew Hastie labelled the response "flat-footed" and "ambiguous".
But the prime minister said the government's position about Iran having access to nuclear weapons had been stated repeatedly.
"What my government does is act in an orderly, coherent way, and we were very clear for some period of time that Iran could not be allowed to have nuclear weapons," he said.
"We called for Iran to come to the table to ensure that the United States wouldn't have to take the action that they took.
"We made clear that we supported action that would ensure that Iran couldn't gain that nuclear weapon."
Mr Trump posted on his Truth Social platform that a "complete and total ceasefire" had been "fully agreed" by Israel and Iran.
He wrote an initial 24-hour ceasefire period, which would progressively begin after already in-progress attacks finished, would mark "an official end to the 12-day war".
Mr Albanese used reports of the ceasefire to also call for de-escalation of Israel's conflict with Hamas in Gaza.
"We also want to see the legitimate aspirations of the Palestinian people fulfilled, and we want to see peace and security in the region. It has been a source of global instability for a long time," he said.
"We support Israel's right to defend itself. We haven't been uncritical of Israel where we believe that the actions have not been consistent."
US bombers dropped bunker-buster bombs on three Iranian underground nuclear sites on the weekend.
In response, Iran targeted the Al-Udeid US air base in Qatar with "powerful" retaliatory missiles on Monday night, local time.
The attacks forced airspace around Qatar to temporarily close, which impacted flights from Australia.
A Virgin Australia spokesperson said the airline's scheduled services to Doha, operated by Qatar Airways, were expected to operate later with delays.
"We are working closely with our partner Qatar Airways to support passengers that have been impacted," they said.
A Qantas spokesman said a Perth to London flight had been diverted to Singapore, while a Perth to Paris service was returning to Western Australia.
"We continue to monitor airspace availability closely and will alter our schedule as required," he said.
Opposition Leader Sussan Ley said a ceasefire was a "vital step" for preventing further suffering, while condemning Iran for its strike.
The government is still trying to evacuate about 3000 Australians registered for assistance to depart Iran and more than 1000 in Israel.
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