The US president criticised allied countries for not providing assistance in the conflict, as the closure of the Strait of Hormuz continues to drive up global oil prices.
"(UK Prime Minister Keir Starmer) didn't want to help us. Australia, too. Australia was not great. I was a little surprised by Australia," Mr Trump said.
Mr Albanese said Australia hadn't been consulted by Washington ahead of its strikes.
"President Trump is someone who I've enjoyed a very constructive relationship with ... but I again reiterate that there is no request being made to Australia," the prime minister told reporters in Canberra on Friday.
"I'm not precious about these things. We made a decision as well about what our response would be, and we continue to engage constructively."
Mr Albanese reiterated the government wanted an end to the war, noting the significant economic impacts.
Australia is providing military assistance in the Persian Gulf region following a request from the United Arab Emirates.
An E-7A Wedgetail surveillance plane, along with 85 defence force personnel, have been sent to the UAE to monitor Iranian drone strikes.
"It is playing an important role in respect of the defence of the gulf states," Defence Minister Richard Marles told the ABC.
"We will work this through with our with our friends and our partners, to look at what role we can play."
The request for help from the UAE had been the only one received by Australia since the US-Israel war with Iran began, Mr Marles said.
"Defending the states of the Gulf is really important given our relationship with them," he said.
The US president has extended a self-imposed deadline to Iran to re-open the Strait of Hormuz to April 6 before potential strikes on energy infrastructure.
Coalition frontbencher Sarah Henderson said the government needed to outline why military help had not been provided to the US.
"It's quite embarrassing that in the international stage we have been called out as not providing appropriate assistance to the US," she told Sky News.
"The US is our strongest defence ally. This is pretty grim news overnight from the United States."
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