Heaping praise on Australia as a strong ally, Mr Trump opened talks with Mr Morrison at the G20 summit in Japan by congratulating him on the outcome.

"He didn't surprise me but he surprised a lot of people," Mr Trump said.

The two met for a working dinner on Thursday night before the opening of the summit on Friday, with fears about a trade war dominating the agenda.

Asked if his approach to foreign policy sometimes looked like "America alone" to allies, Mr Trump insisted the US looked after its friends.

"We take care of our allies," the President said, before citing talks on trade with Australia as an occasion where both sides emerged happy.

The decision to hold the dinner surprised some American observers, given Mr Trump's focus on his policy on Iran at this summit, with bilateral meetings arranged with leaders from Russia and Saudi Arabia.

Mr Morrison will use a series of high-stakes meetings with global leaders in the next two days to redouble Australian efforts to reform world trading rules, making a direct plea to Mr Trump to halt a growing dispute with China.

The Australian position backs the need to overhaul trading rules just as Mr Trump and Chinese President Xi Jinping inch toward a temporary truce after months of increasing tariffs and fuelling fears of an economic downturn.

As leaders arrived in Japan, reports emerged that Chinese and US officials were canvassing options such as delays to additional US tariffs to ease the way for a truce when Mr Trump and Mr Xi meet on Saturday.

Mr Morrison goes into the summit with support from France and Canada on his proposal for stronger rules on social media giants to stop the spread of live video of terrorist attacks.

But the threat to the global economy is expected to be the dominant subject at the annual summit, giving all leaders a forum to press Mr Trump and Mr Xi to reach a settlement.

Mr Morrison said all the leaders had a "critical stake" in making sure the trading system was durable.

"The alternative does not bear contemplation," he said ahead of his meeting with Mr Trump.

"This means we all have a part to play in solving the problems the system faces.

"The system needs the confidence of its members and clearly that is no longer the case. We can't let that mean we slip into a further deterioration in key trading relationships and the collateral damage that would bring."

In a worrying sign for Australian relations with China, there is no bilateral meeting scheduled between Mr Morrison and Mr Xi and there was no such meeting at the last G20 summit, held in Argentina last December.

Mr Morrison held a formal meeting with Chinese Premier Li Keqiang in Singapore last December.

Finance Minister Mathias Cormann said on Thursday it was not possible to hold a bilateral meeting with every leader at every G20 but he confirmed there was no meeting with Mr Xi.

"This time around, we are having a dinner with President Trump but there is no scheduled meeting with the President of China," Senator Cormann said.

The meeting between Mr Morrison and Mr Trump was scheduled to be one of the biggest of its kind in recent years, with Senator Cormann and Trade Minister Simon Birmingham joining the group along with the Australian ambassador to the United States, Joe Hockey.

Those attending from the US side were expected to include Secretary of State Mike Pompeo, Treasury Secretary Steve Mnuchin, National Security Advisor John Bolton, US Trade Representative Robert Lighthizer and Mr Trump's daughter and adviser Ivanka Trump.

Mr Morrison intends to use his remarks to the opening session of the summit to make the case for reforms to update World Trade Organisation rules, against the backdrop of US criticisms at the way China gains from open trading by other countries while maintaining protections of its own.

Australia will back the case for new rules at the WTO on electronic commerce as a way to show that the negotiating body can settle differences in a better way than the tariff war between the US and China.

Even so, the draft communique for the Osaka summit does not appear to raise ambitions for free trade compared to the outcome of the Buenos Aires summit last December, where the Trump administration ensured the final statement dropped a commitment to "fight protection" - a pledge included in similar documents in the past.

The draft Osaka communique is said to leave out the same words.

"It is in nobody's interest for there to be an ongoing and sustained trade war between the US and China," Senator Cormann said in Osaka on Thursday.

"It is not in the US's interest, it is not in China's interest and we certainly hope that sense and sensibility will prevail."