The G-20 countries represent 85 percent of the global gross domestic product, two-thirds of the world's population, and 75 percent of worldwide trade. Those divisions have highlighted the fractures in the grouping.
The summit was held in tight security conditions, following threats of violent disruption from some groups in Buenos Aires.
But their initial meeting was overshadowed by the warm embrace between Russian President Vladimir Putin and Saudi Crown Prince Mohammad Bin Salman, who high-fived each other at the beginning of the forum.
Taking the world stage at the G-20 could be welcome relief for some leaders dealing with challenges back home.
What can Crown Prince Mohammed expect?
The Saudi leader has been the subject of widespread condemnation after Washington Post journalist Jamal Khashoggi was killed during a visit to the Saudi Arabian consulate in Turkey in October. Saudi Arabia has blamed "rogue agents" but suspicion has fallen on the prince for ordering the killing.
He declined to say what other US officials will join Trump in the session.
"Now, trade, climate, migrants, refugees, multilateralism, steel - which are really the thorny issues - remain without agreement".
After the address, the leaders stayed for the afternoon plenary session.
The President was accompanied, in addition to the First Lady, by his daughter and advisor, Ivanka Trump, and his son-in-law and advisor, Jared Kushner, as well as by U.S. Secretary of State Mike Pompeo and the White House Chief of Staff John Kelly.
What will go on on the sidelines?More news: Trump says Putin meeting may be called off over ‘aggression’ against Ukraine
Mr Putin, he said, "is ready to have contacts with his American counterpart".
"We don't like what happened".
Mr Putin's spokesman, Dmitry Peskov, said Moscow regretted the decision.
Tough talking is expected at the summit, especially between Trump and Xi Jinping of China, over global trade.
The second-highest profile meeting will also involve Mr Trump.
Navarro's presence at the dinner might signal an agreement is less likely, though Trump has suggested the final result of the meeting will largely depend on the leaders themselves. -China trade dispute to the conflict over Ukraine.
The United States and China are exploring a trade deal in which Washington would suspend further tariffs through the spring of 2019 in exchange for new talks "looking at big changes in Chinese economic policy", the Wall Street Journal reported on Thursday. There are some good signs. U.S. steel producers have welcomed the taxes, as they've seen prices for their own products go up. The Russian president condemned "dishonest competition" along with "vicious" sanctions and protectionist measures.
The US is also undermining the World Trade Organisation by refusing to appoint new trade judges, leading WTO boss Robert Azevedo to declare global trade is in its worst crisis since 1947.
"All of our countries will benefit greatly", he said.
Trump has already bared its disdain for worldwide summitry by blocking final communiques at other recent gatherings such as the G7 and the Asia-Pacific bloc APEC, setting the stage for a fractious G20 on Friday and Saturday.
Mr Trump has not hidden his objection to collective action on the issue.