"The easiest thing I can do – in fact,I could do it while you're here – would[be to] say:'Go ahead,fellas. Go do it,'"Mr Trump said while speaking to reporters alongside Mr Morrison in the Oval Office.
"And that would be a very bad day for Iran. That’s the easiest thing I could do. It's so easy."
He added,however,that he was not looking to take that action if it could be avoided.
US Treasury Secretary Steven Mnuchin announced further sanctions against Iran on Friday that he said would"cut off all source of funds to Iran"by blocking transactions with the nation’s central bank.
Australia has backed the US action against Iran in the Persian Gulf by committing a frigate and a surveillance aircraft to prevent the seizure of commercial tankers in the Strait of Hormuz.
While Mr Trump said he was"always prepared"for stronger military action against Iran,Mr Morrison said the question was"moot"when asked if he was open to further military commitments.
"There are no further activities planned or requested for assistance from Australia,so the question to that extent is moot,"he said.
"The calibrated,I think,very measured response that the United States is taking has been a matter for them and obviously at any time when issues are raised with us as an ally,we consider them on their merits at the time in Australia’s national interests."
Soon after the meetings in the White House but beforea formal state dinner for Mr Morrison on Friday night,Mr Trump authorised the deployment of additional US forces to the Middle East to strengthen air and missile defences around Saudi Arabia and the United Arab Emirates.
The announcement underscored the growing tensions in the region following an attack last week on Saudi Arabian oil plants,leading the US and Saudi Arabia to blame Iran for the strikes.
In a signal of stronger US military action to come,US Defence Secretary Mark Esper described Friday’s deployment as a first step in response to requests for help from Saudi Arabia and the UAE.
Mr Trump lavished praise on Mr Morrison when asked about a remark in 2003 when former president George W. Bush described former prime minister John Howard as a"man of steel"for standing his ground.
"I would say a man of titanium,"Mr Trump said."You know,titanium is much tougher than steel. He's a man of titanium. Believe me,I have to deal with this guy. He's not easy.
"You might think he's a nice guy,okay? He’s a man of real,real strength,and a great guy. And his wife is lovely."
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The report inThe Wall Street Journal on the state visit saidMr Morrison wanted Mr Houston to attend events but this was blocked by the White House.
"After several rounds of discussions across the 14 time zones between Washington and Canberra,Mr Morrison agreed to leave the pastor at home,according to several people familiar with the matter,"theJournal reported.
A spokesman for Mr Morrison toldThe Sun-Herald andThe Sunday Age the guest list was a matter for the President.
"Invitations to the state dinner are entirely at the discretion of the White House as has been the case previously,"he said.