With shops, schools and business shuttered as Arab towns and villages observed a general strike, police raised the alert to one below the highest level and deployed in areas of friction, spokeswoman Luba Samri said.
The protests began early Saturday after police shot dead a 22-year-old in Kfar Kana near the northern city of Nazareth.
Kheir Hamdan was killed after he attacked police with a knife as they tried to arrest a relative.
Relatives say Hamdan was killed "in cold blood", with CCTV footage apparently contradicting the official version.
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In the footage, a man in a white T-shirt is seen banging on a police van window with a knife for about 10 seconds before starting to run off as a man gets out of the back door.
The man fires his gun as he walks towards Hamdan, and officers drag his body into the vehicle.
The shooting brought angry crowds onto Kfar Kana's streets where around 2,500 people demonstrated as youths threw stones and burned tyres.