In her first telephone conversation with Mr Trump after he took office, she explained that the Geneva Convention obliges signatories, including the US, to take in refugees of war on humanitarian grounds.
Mrs Merkel also had a strong relationship with Barack Obama. His final call to a foreign leader as president was said to be to Mrs Merkel, thanking her for her leadership.
BBC Berlin correspondent Jenny Hill says Mrs Merkel and Mr Trump are also two leaders with hugely different styles - he is flamboyant, impetuous and prone to rhetoric, while she is reserved, pragmatic and lingers over decisions.
Our correspondent says Angela Merkel needs to walk a diplomatic tightrope. She has to build a working relationship with Mr Trump without appearing to sacrifice her own values or disappoint those keen to cast her as the West's last defender of those democratic ideals.
This first meeting comes as she prepares for an election battle later in the year, seeking a fourth term as chancellor.
Trade is a key issue for the summit.
During his presidential campaign, Mr Trump threatened higher import taxes for countries such as Germany that have a trade surplus over America.
Mrs Merkel is being accompanied by top executives from German companies Siemens, Schaeffler and car giant BMW and will point out the large direct German investment in the US.
She said BMW's plant in the US exported "more cars than GM and Ford together" from the United States, adding: "I'll make that clear."
On Friday morning, Economy Minister Brigitte Zypries said Germany could file a suit against any hike in import duties at the World Trade Organization (WTO).
"There are procedures laid out there because in the WTO agreements it is clearly laid out that you're not allowed to take more than 2.5% taxes on imports of cars," Ms Zypries told Deutschlandfunk radio - Mr Trump has suggested a 35% levy.
"It wouldn't be the first time that Mr Trump has lost in the courts," she added.
Nato is also on the agenda.
Mr Trump has insisted members pay their fair share. Only four nations currently reach the benchmark of spending 2% of GDP on defence. Germany is not among them.
The agenda is also expected to cover foreign policy issues involving Russia, Syria, Iran, North Korea and the Middle East peace process