"There is no place for racism and discrimination in (our) society, none," Netanyahu said at the annual commemoration for around 4,000 Jews who died while trying to flee their homeland for Israel in the early 1980s.
They perished while en route to the Ethiopian-Sudanese border where they waited in transit camps to be airlifted to Israel, with around 8,000 survivors completing the journey.
"We shall fight with all possible force against this unacceptable phenomenon. We shall simply uproot it from our lives," he told an audience containing many Ethiopian immigrants, some in tears as they recalled those who died trying to reach the Jewish state.
Subsequent waves of immigration and the birth in Israel of a new generation have brought today's Ethiopian-Israeli community to about 135,500 people.
However, in the past few weeks, thousands of Ethiopian Jews have taken to the streets to express their anger over alleged police brutality and racism, which Netanyahu has pledged to tackle.
Two main rallies, one in Jerusalem and one in Tel Aviv, were sparked by video footage showing police manhandling an Ethiopian-Israeli soldier in uniform.
Signup to our newsletter and follow us on Facebook and Twitter!
At the Tel Aviv protest, riot police, some on horseback, used stun grenades, water cannon and pepper spray to disperse thousands of angry demonstrators who threw stones, bottles and chairs.
Many of the immigrants live in the poorest quarters of major cities. More than a third of Ethiopian-Israeli families live below the poverty line, and many are in menial jobs.
"In recent weeks we have all seen and heard the cries and pain of Israelis of Ethiopian origin," Rivlin said at the memorial ceremony.
"The protesters uncovered an open wound, alive and bleeding within Israeli society.
"We heard a wounded community who voiced their heartfelt cries of feelings of discrimination, racism, insult and lack of response."
"Israel erred in the integration and treatment of the Ethiopian community along the years," he added.
"We didn't see, we didn't act correctly, we didn't listen enough."