President Barack Obama said the nation needed to do “soul-searching” on the shooting death of Florida teenager Trayvon Martin and said authorities would treat the case with the seriousness it deserves.

“When I think of this boy, I think about my own kids,” Obama said. “I can only imagine what his parents are going through. … If I had a son, he’d look like Trayvon.”

Obama said “all of us have to do some soul-searching” on how something like this happens.

In remarks he addressed to Martin’s parents, Obama said federal, state and local officials should work together to investigate the case.

“We’re going to get to the bottom of exactly what happened,” he said.

The shooting, and lack of an arrest, has sparked protests across the country and a demand from the Congressional Black Caucus for a federal investigation, which is now under way. Martin was reportedly unarmed when a neighborhood watch captain shot him in his neighborhood.

Obama made the remarks in response to a reporter’s question at a Rose Garden ceremony to announce his pick to head the World Bank, Dartmouth College President Jim Yong Kim.