Merkel and Trump discussed climate issues, the Women's Entrepreneurship Financing Initiative, and trade, including the global steel overcapacity, the statement said.
Before meeting with his counterparts, President Trump has called on numerous global leaders with regard to disputed issues.
After President Trump's forthright opinions that Chancellor Merkel is "ruining" Germany, the relationship between Berlin and the White House cooled significantly.
"We know the positions of the USA government and I do not expect them to disappear on a two-day trip to Hamburg", the chancellor said.
A three-time world leader who has been criticized as being too soft on the policies of the current USA president, Merkel observed that Trump's anti-globalization posture serves to exacerbate the belief that only "winners and losers" populate the global financial architecture, ignoring the possibility of a "win-win situation" in which all nations benefit. In its new manifesto the CDU/CSU refers to the relationship as Germany's most important "partnership" outside Europe.
Greenpeace, for example, regards the G-20 as a chance for the leaders to send a strong signal about fighting climate change - despite the Trump administration's decision to pull out of the Paris agreement on reducing emissions.
At the event Sunday, spearheaded by 170 organizations and parties united thousands under the slogans "Solidarity without borders instead of G20", "Stop Coal", "Fight Poverty", demonstrators walked together to protest the meeting of worldwide heads and "global capitalism".
On Monday, Trump said of his call with King Salman, "Interesting things are happening!" but did not elaborate.
The G20 Hamburg Summit is a reunion of leaders of the world's most important 20 economies after the Hangzhou Summit, which was held previous year.
Tens of thousands of protesters are expected to march in the city against globalisation and what they say is corporate greed and a failure to tackle climate change.
Even in the United States, more people have confidence in Merkel than in their own president (56 percent to 46 percent).