Obama took a veiled shot at Trump over his comments about Muslims
"In some places, including the United States, we've seen the rise of dangerous political rhetoric that targets immigrants or Muslims," Obama said.
The interview was conducted by Kai Diekmann, publisher of BILD and a Business Insider contributing editor, and Tanit Koch, editor in chief of BILD.
Obama's reference to anti-Muslim rhetoric is likely at least in part a reference to Trump's proposed ban on Muslims entering the US.
Late last year, the frontrunner for the Republican presidential nomination called for the US government to bar most Muslim tourists and immigrants from entering the US until the terrorist "problem" is under control.
"The politics around refugees and immigration is hard in any country, but I believe the best leaders are willing to take on the toughest issues - especially when it's not easy," Obama said in the interview. "... We cannot simply shut our doors to our fellow human beings when they are in such desperate need. That would be a betrayal of our values."
In another possible reference to Trump's statements, Obama said the US can protect its security with the checks it does on refugees entering the country.
"We know how to do this responsibly in a way that ensures our security, including extensive checks so we know who we're welcoming to our country," Obama said.
Trump has repeatedly cautioned against accepting refugees into the US on the grounds that "we don't know who these people are."
In the interview, Obama praised German Chancellor Angela Merkel, whose government has faced staunch opposition for accepting hundreds of thousands of refugees from war-torn Syria.
"I believe that Chancellor Merkel's approach to the refugee crisis - and that of many Germans - has been courageous," he said.
Obama also emphasized in the interview the importance of the North Atlantic Treaty Organization, an alliance that Trump has said is "obsolete."
He said "our NATO allies are playing a critical role in the military campaign" against the terrorist group ISIS. And he added that the US needs Europe "to help uphold our Article V commitment to our NATO allies and to keep supporting Ukraine's ability to ensure its security in the face of Russian aggression."