Traveling to Washington with Merkel are CEOs of some of the top German companies with workers in the US, including car-maker BMW and tech company Siemens.
The two leaders tried to express their common bonds but showed minimal rapport in their first encounter, a departure from Merkel's warm relations with Obama during his eight years as president.
Merkel said she was in agreement with Trump that "trade has to be fairer, has to be a win-win situation".
Asked whether the USA would provide military defence to Baltic countries if Russian Federation were to attack, Trump said: "If they fulfil their obligations to us, the answer is yes".
Trump had made European defence spending an issue during his campaign, saying the United States - which spends just over 3% of its GDP on defence - carries too much of the financial burden for supporting North Atlantic Treaty Organisation.
During the White House meeting, Merkel pledged to continue to increase Germany's defense budget and reaffirmed her country's commitment to the 2 percent goal by 2024.
Trump and Merkel tried to sidestep their differences in their meeting at the White House on Friday, but it was punctuated by some awkward moments. "When we talk about trade talks, the European Union negotiates for all of the member states in the European Union", she said.
Thinking he hadn't heard, Merkel appears to gently asks him: "Do you want to do the handshake?"
Trump has been critical of Merkel in the past, especially for her decision to accept large numbers of refugees.
"We're still in the phase of trying to figure out how the new administration is going to work in terms of the conflicting messages coming out of the different power centers in the White House and the different agencies", said Sudha David-Wilp, a senior transatlantic fellow at the German Marshall Fund in Berlin.
Downing Street later said that Trump had offered May his hand as they walked down a ramp in a "chivalrous gesture".
"Germany's like sitting back silent collecting money and making a fortune with probably the greatest leader in the world today, Merkel", Trump told Time.
On economic matters, the Chancellor said she hoped Trump would consider re-opening discussions on the TransAtlantic Trade and Investment Partnership, a proposed pact between the USA and the European Union. Angela looked on as if he had mispronounced her name (which, let's face it, there's a probability of!). "The negotiators for Germany have done a far better job than the negotiators for the United States", Trump said.
Since he began his campaign for the U.S. presidency, Trump has regularly used Twitter to make sweeping and contentious remarks in which he outlines changes of direction in domestic and foreign policy.