Trump described Merz as a good representative of Germany and also "difficult," which he suggested was a compliment.
He said US troops would remain in Germany and said it was positive that the government there was spending more money on defence.
Merz said he was pleased to be there and preparing for a deeper relationship with the United States.
The two leaders met in the Oval Office, which has been the site of showdowns between Trump and visiting dignitaries including Ukrainian President Volodymyr Zelenskiy and South African President Cyril Ramaphosa.
Not so on Thursday.
Trump and Merz, both conservatives, appeared to have a warm rapport from the start.
Merz started with praise, thanking Trump for putting him up in the Blair House, a presidential guest dwelling across from the White House, and Trump thanked him for doing so.
But tensions over trade simmered under the surface of their encounter.
The United States and the European Union are in talks to reach a trade deal, which would be critical for Germany's export-heavy economy, but Trump said he would be fine with an agreement or with tariffs.
"We'll end up hopefully with a trade deal," Trump said.
"I'm okay with the tariffs or we make a deal with the trade."
Merz, who took office last month, told reporters ahead of the meeting that they would discuss Russia's war in Ukraine, US tariffs and the NATO military alliance in the meeting but said he was not expecting major breakthroughs.
Germany is the second largest military and financial backer of Ukraine in its defence against Russia's invasion, after the United States.
Merz and Trump could find some common ground given they share business backgrounds, membership in conservative political parties, a focus on fighting illegal immigration and a fondness for golf, said Steven Sokol, president and CEO of the American Council on Germany.
