Benjamin Netanyahu spoke after meeting Ethiopian Israeli community leaders and an Ethiopian Israeli soldier, whose beating by police has fuelled tensions.
A protest by Ethiopian Israelis on Sunday ended in clashes with police.
Israel's president said the community's grievances "revealed an open and raw wound" at the heart of Israeli society.
"We must look directly at this open wound," Reuven Rivlin added. "We have erred. We did not look, and we did not listen enough."
At least 46 police and seven demonstrators were hurt in the clashes which followed the protest in Tel Aviv on Sunday night, officials said. Dozens of protesters were arrested, police said.
Call for unity
On Monday, Mr Netanyahu met Israeli soldier Damas Fekade, who was beaten by two police officers in a suburb of Tel Aviv last week.