"He's a man of titanium, believe me, I have to deal with this guy.
"You might think he's a nice guy, OK, he's a man of real, real strength and a great guy."
Earlier, the Trumps welcomed the Morrisons to America with full military pomp and circumstance on the South Lawn of the White House.
"Today we vow to carry on the righteous legacy of our exceptional alliance," Mr Trump told the gathered crowd of about 4500 people.
That alliance stretched back over more than a century of joint military operations, both leaders noted.
"From the woods of Le Hamel to the jungles of Southeast Asia to the dust of Tarin Kot in Uruzgan, and now the waters of the Strait of Hormuz, Australians and Americans have always stood together," Mr Morrison said.
The joint operations in the waters south of Iran are a major topic of conversation for the leaders and their officials during the top-level meeting on Friday.
Mr Trump said he thought the US had taken a "very measured and calibrated approach" towards the Middle Eastern nation.
Mr Trump then repeatedly suggested he could make the call to go to war against the Middle Eastern nation right then and there with Mr Morrison and the media pack in the room.
"The easiest thing I can do, in fact, I can do it while you're here, is say, 'go ahead fellas, go to them'. And that would be a very bad day for Iran," he said, after announcing stronger economic sanctions on Iran.
Australia has so far agreed to a limited contribution to the US-led freedom of navigation operation in the Strait of Hormuz.
The talks between the leaders are also expected to encompass trade and the tensions with China, co-operation on the US plans for space missions to the moon and Mars, and rare earth exports.
"For a century we have done what true friends do - stick by each other," Mr Morrison said at the welcome ceremony.
"Whatever lies ahead in this century, I know that Australia and the United States will go on to meet it with the same courage, the same daring, and the same unbreakable bond that has defined the first century of mateship."
He leaves a visual reminder of this long friendship, giving Mr Trump a statue of WWII soldier Leslie "Bull" Allen carrying a wounded American off the battlefields of Papua New Guinea.
The pair have spoken about Corporal Allen's story twice previously and for Mr Morrison, it symbolises the indelible bonds that tie the nations together.
Later Mr Morrison will be honoured, first with a luncheon for about 220 guests hosted by Vice-President Mike Pence and Secretary of State Mike Pompeo at the State Department, and then with an official state banquet in the gardens of the White House.
He is expected to delve further into the important economic ties at the State Department lunch, noting the US has had a trade surplus with Australia - selling more Down Under than it buys - since the Truman administration.
"All US exports enter Australia tariff-free and quota-free. You can't get a better deal than that," he will say, according to speech notes.
"We are the gold standard of US trade partners."
Prime Minister and President #auspol #uspol 🇦🇺🇺🇸 @SBSNews pic.twitter.com/XAOVZyqrkE
— Brett Mason (@BrettMasonNews) September 20, 2019