"Israel is facing a wave of murderous Arab terror," Prime Minister Naftali Bennett tweeted after Tuesday's shootings in Bnei Brak, a Jewish ultra-Orthodox city on the outskirts of Israel's commercial capital.
The shooting raised to 11 the number of people killed by Arab gunmen in Israel during the past week, the sharpest spike in attacks on city streets in years.
Palestinian President Mahmoud Abbas condemned the killing of Israeli civilians and stressed the killing of Israelis and Palestinians would only lead to a deterioration of the situation, cautioning against retaliatory attacks by Jewish settlers and others.
Palestinians have been reporting a rise in settler violence across the West Bank and East Jerusalem, which Israel captured in a 1967 war.
Amateur video broadcast on Israeli television showed a man dressed in black and pointing an assault rifle walking down a road in Bnei Brak.
Witnesses said he began shooting at apartment balconies and then at people on the street and in a car.
Israeli media reports said the assailant was a Palestinian from a village near the city of Jenin in the occupied West Bank.
Police said he killed four civilians and an officer who had arrived on the scene before police fatally shot him.
Israeli officials had cautioned about a surge in assaults in the run-up in April to the Muslim holy month of Ramadan, a time when violence has surged in the past.
Palestinians and Israeli police and settlers clashed nightly during Ramadan last year. Police raids at Al-Aqsa mosque compound and a ban on evening gatherings at Damascus Gate helped ignite violence between Israel and Gaza militants that led to 11 days of Palestinian rocket attacks and Israeli air strikes.
Last week, an Arab citizen of Israel killed four people in a stabbing and car-ramming attack in the southern city of Beersheba, before he was shot dead by a passer-by. Israeli authorities said he was an Islamic State sympathiser.
On Sunday, as an Israeli-Arab summit convened in southern Israel, an Arab assailant shot and killed two police officers in Hadera, a city north of Tel Aviv. Other officers shot and killed him.
Islamic State claimed responsibility for the attack.