The prime minister spoke to the president ahead of a key meeting at the summit between Mr Trump and Chinese President Xi Jinping.
The group of 20 accounts for 85% of the world's GDP and two-thirds of its population.
Argentina's leader thanked President Trump for his visit and for his support of the South American nation.
Beijing hopes to persuade Trump to abandon plans to increase tariffs on $200 billion of Chinese goods to 25 percent in January, from 10 percent at present. China has imposed retaliatory tariffs on around $US110 billion of U.S. goods.
Following hopes that a deal would be made between the two countries, USA stocks closed higher on Friday.
"We are in a position to deal with it and handle it very well", he told reporters.
'In the past they've sought to take a fairly orthodox approach. what we've seen more recently you wouldn't describe as orthodox, but that doesn't mean the objective isn't the same, ' Mr Morrison said.
"We've just gotten to know each other and, so far, so good", was his estimation of Mr Morrison from the outset, before adding "I think it's going to be a great relationship". China calls the United States protectionist and has resisted what it views as attempts to intimidate it.
President Trump said recently that current tariff levels on $200bn (£157bn) of Chinese imports would rise as planned.
Argentine officials are distancing themselves from the United States version of how they view China trade after a meeting during the Group of 20 summit.
Trump has cast his talks Saturday with Xi as a deadline for China to cave on his key trade concerns, including access for U.S. companies and protection of their intellectual property.
More moderate aides such as Mnuchin and National Economic Council chairman Larry Kudlow have advocated for easing trade tensions with China, offering warnings that escalating the trade war would only make matters worse, and allow Trump's critics to pin even more of the blame for a shaky economy on him.
The New York Times has described Mr Trump as "lonely" at the world summit and said his only friend was Mr Morrison.More news: Syria state TV says air defenses repelled missile attack
Trump cited Russia's seizure of the ships as the reason he cancelled a planned bilateral meeting with Russian President Vladimir Putin, where they had been expected to discuss the USA leader's threat to withdraw from the Cold War-era Intermediate-Range Nuclear Forces treaty.
Mr Trump said he would not meet the Russian leader "based on the fact that the ships and sailors have not been returned".
It's in these sessions that he's most likely to run across Saudi Crown Prince Mohammed bin Salman, who most of the world has castigated after the murder of journalist Jamal Khashoggi.
Human Rights Watch is also waiting for the crown prince, having urged Argentine prosecutors to charge him with war crimes over the Saudi-led military coalition's action in Yemen.
Putin would be one of several leaders to meet the Saudi prince, who is also expected to hold talks with Turkish President Recep Tayyip Erdogan and United Nations chief Antonio Guterres.
Saudi Arabia maintains that the Crown Prince had no knowledge of the killing.
"Capitalism and the G20 want to exploit the natural resources and force us to work from 12 to 14 hours a day", said Osmar, a Bolivian protester who lives in Argentina.
Uncertainty prevailed about how Trump, known for his unpredictability, would behave at what was shaping up as one of the group's most consequential summits.
Meanwhile, oil markets anticipated a bilateral meeting between Putin and Prince Mohammed on Saturday for a sign that Russian Federation will participate in a production cut by the OPEC oil cartel next month.
The G20 brought another first Mr Morrison, through his introduction to French President Emmanuel Macron.
A Chinese foreign ministry official in Buenos Aires said there were signs of increasing consensus ahead of the discussions, although differences remained, Reuters reported.
The three countries agreed a deal in principle to govern their trillion dollars of mutual trade after a year and a half of contentious talks concluded just an hour before a deadline on September 30. But on Thursday evening, an official with the Canadian Prime Minister said Trudeau would be at Friday's ceremony. As of now, there is no certainty on the deal, the daily said citing unnamed governmental sources.