Many demonstrations took place at road junctions causing long delays to traffic.

Police had initially taken a permissive stance opposite the protests.

"Over the last days the police have allowed demonstrations to take place and let protesters openly demonstrate. Police have carried out an open dialogue with the leaders of the community in order to prevent riots and violence against police or civilians," a police statement said.

It went on, "Police are now responding by dispersing the protests and preventing further riots and acts of danger to policeman and civilians."

An investigation into the precise circumstances of Sunday's shooting is underway.

An initial statement by police about the incident -- challenged by eye-witnesses, according to reports in Israeli media - said the off-duty officer described seeing a fight in a playground.

After approaching the people involved in the fight and telling them he was a police officer, they started throwing stones at him, the police statement said.

The off-duty officer found himself in a life-threatening situation, the statement said, and he opened fire.

Israeli media reports say Solomon Teka was 19 years old.

Israel's President, Reuven Rivlin, who has spoken often about his wish to see greater social cohesion in Israel, addressed the country's Ethiopian community directly, and appealed for calm.

In a statement, he said, "I ask all of us to act responsibly and with moderation. I know that you are doing everything in your power to convey the voice of your protest and to lead a change that is all about righting wrongs and creating a better future. No one wants revenge. The agitation comes from a deep rift and a great prayer for making things better. We are all partners, we must all be partners in this process. We have no other choice. We have no other home."