"I think we'd like to", said President Trump before heading into a meeting with Japanese Prime Minister Shinzo Abe.
What they agree on - or do not - will likely determine whether stock markets rise or fall and whether the world economy gets some relief from destabilizing trade tensions, as well as cast judgement on the wisdom of the USA leader's hard-nosed trade tactics.
Trump was attacked for destroying the group's past unity on trade and climate change.
President Donald Trump on November 30 lauded "good signs" ahead of talks with his Chinese counterpart Xi Jinping on resolving their trade war.
Putin was the only leader to exchange an openly cordial greeting with the isolated Saudi prince, high-fiving him when he entered the main summit room, news reports said.
"Five years ago, when I first attended the G20 leaders' summit, I called for the maintenance and development of an open world economy", Xi said, according to a transcript of his speech.
They also protested against the amount spent on the summit at a time when Argentina is in an economic crisis and against President Mauricio Macri's policies to combat inflation. When a meeting does happen, Putin said there will be no preconditions.
The G20 brought another first Mr Morrison, through his introduction to French President Emmanuel Macron.
Apart from trade and climate change, Russia's seizure of Ukrainian vessels drew condemnation from other G20 members, while the presence of Crown Prince Mohammed bin Salman at the summit raised an awkward dilemma for leaders.
The summit marks a quick return to the worldwide stage for the Prince Mohammed after the kingdom came under fire for the killing of journalist Jamal Khashoggi in its Istanbul consulate.
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Saudi Arabia has insisted the prince had no prior knowledge of the killing.
Fast-forward three years and he's hosting this summit in a new political era - one where protectionism and populism, not globalisation, are the order of the day.
European Council President Donald Tusk was more focused on the Ukraine crisis, saying he was "sure" the bloc would roll over its sanctions on Russian Federation next month.
USA objections on those fronts have seen two major summits this year, of the Group of Seven democracies and the Asia-Pacific Economic Cooperation forum, end without the once-routine statements.
The same disputes were hobbling adoption of a G20 communique, observers said.
US Secretary of State Mike Pompeo and Saudi Foreign Minister Adel al-Jubeir discussed the need for progress in the investigation into slain journalist's brutal killing and dismemberment during talks in Buenos Aires on Friday, the US State Department said in a statement.
Leaders of the United States, Canada and Mexico, meanwhile, met in the morning to sign a trade deal replacing the North American Free Trade Agreement that was struck following months of tough negotiations that analysts say left a bitter taste among the partners.
Ahead of the G20 Mr Trump told U.S. media he expected to go ahead with plans to raise tariffs on $200bn of Chinese goods - first introduced in September - to 25% (up from 10%) starting in January 2019. There could also be confrontation between the American and Putin over the escalating confrontation in Ukraine, which caused Trump to cancel a planned meeting with Putin.
"If we did that with cars coming in, many more cars would be built here and GM would not be closing their plants in Ohio, Michigan & Maryland", Trump tweeted, adding that "The President has great power on this issue".
Argentina has deployed around 25,000 police officers and soldiers to prevent violence similar to that seen during last year's G20 summit in Hamburg, Germany, when hundreds of police officers were injured.