Prime Minister Anthony Albanese on Tuesday welcomed the news posted by Mr Trump on social media that a ceasefire would take effect within hours following 12 days of conflict.
"We have consistently called for dialogue, diplomacy and de-escalation," Mr Albanese said.
"The safety of Australians in the region is our priority.
"We continue to closely monitor the situation in the Middle East and are deeply concerned about keeping Australians safe."
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 any already in-progress attacks finished, would mark "an official end to the 12-day war".
But Iran's Foreign Minister Seyed Abbas Araghchi disputed the ceasefire on the social media site X.
"As of now, there is NO 'agreement' on any ceasefire or cessation of military operations," he wrote.
"However, provided that the Israeli regime stops its illegal aggression against the Iranian people no later than 4am Tehran time, we have no intention to continue our response afterwards.
"The final decision on the cessation of our military operations will be made later."
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 their Perth to London flight had been diverted to Singapore, while Perth to Paris was returning to Western Australia.
"We continue to monitor airspace availability closely and will alter our schedule as required," he said.
US bombers dropped bunker-buster bombs on three Iranian underground nuclear sites one the weekend, joining Israel's conflict against Iran.
In response, Iran targeted the Al-Udeid US air base in Qatar with "powerful" retaliatory missiles on Monday night, local time.
Qatar's government successfully intercepted the missile attack and no deaths or injuries were recorded.
Foreign Minister Penny Wong earlier condemned Iran's attack.
"We do not want to see further escalation," she wrote on X.
"A full-scale war in the Middle East would be devastating for the people of the region and the world."
US military officials said none of its bases in Iraq were targeted, although a malfunctioning Iranian missile aimed at Israel triggered an alert in Iraq earlier in the day.
Opposition Leader Sussan Ley said a ceasefire was a "vital step" for preventing further suffering, while condemning Iran for its strike.
"Australia must always stand firmly with our allies and partners, including the United States, in the face of such aggression," she said.
Senator Wong urged Australians travelling abroad to register with Smartraveller.
Mr Albanese on Monday publicly supported the US intervention in Iran's west, saying Iran could not be allowed to develop nuclear weapons.
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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