Rivlin made a first gesture, describing community members as “some of our finest sons and daughters” and denouncing their treatment.
“The protesters... revealed an open and raw wound at the heart of Israeli society. The pain of a community crying out over a sense of discrimination, racism, and of being unanswered,” he said.
“We have made mistakes. We did not look, we did not listen enough,” Rivlin said.
Fentahun Assefa-Dawit, executive director of Tebeka, an advocacy organisation for equality and justice for Ethiopian Israelis, said resolving the community’s problems should be Netanyahu’s top priority.
“We call on the prime minister to take matters into his own hands,” he told reporters before heading into talks with the premier.
“We demand him to bring these issues to an end, to establish a committee to investigate everything and plan a way to resolve these issues,” he said.
Earlier on Monday, police went on alert after demonstrators pledged to stage another protest near Netanyahu’s office, but the rally failed to materialise with less than 10 people there, an AFP correspondent said.
It was not immediately clear whether organisers had cancelled the protest or merely delayed it.
Sunday’s demonstration saw protesters blocking a major Tel Aviv highway during rush hour, with police putting their numbers at around 3,000 people.
Organisers said closer to 10,000 people took part.
For centuries, Jews in Ethiopia were largely cut off from other Jewish communities, and Israel’s religious authorities only belatedly recognised them as members of the faith.
Israel began bringing them to Israel in 1984 under the Law of Return, which guarantees citizenship to all Jews.
That operation was largely completed by 1991.
Since their arrival, they have consistently complained of discrimination, with complaints ranging from lower salaries than other Israelis and much higher rates of incarceration, particularly among young people.
The community’s grievances were highlighted in 2013 when Israel’s equivalent of the Red Cross refused to accept blood from an Ethiopian Jewish lawmaker, citing a blanket ban on donations from Israelis born in Africa.