Benjamin Netanyahu spoke after meeting Ethiopian Israeli community leaders and an Ethiopian Israeli soldier, whose beating by police has fuelled tensions.
Israel’s prime minister has said racism in the country must be eliminated, after protests by Ethiopian Israelis against alleged discrimination.
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.
The prime minister praised Mr Fekade and told him he had been shocked by the video of the beating.
Afterwards, Mr Netanyahu met Ethiopian Israeli leaders in an effort to reassure the community.
“We must stand together as one against the phenomenon of racism, to denounce it and eliminate it,” he said.
One of the policemen involved in Mr Fekade’s beating has been dismissed and the other suspended from the force, Israeli police spokesman Micky Rosenfeld told the BBC.
An investigation into the incident is under way.