One person has been killed and five others wounded after a man in a car opened fire at several locations in Israel, authorities say.

Israel's emergency service organisation Magen David Adom (MDA) said a man aged about 35 had died of gunshot wounds. Two of those injured were in a serious condition and three were in a moderate condition "with penetrating injuries to their bodies", MDA said.

The alleged attacker, identified as an Israeli Arab, was killed by security forces near the town of Kokhav Yair, not far from the occupied West Bank.

Police chief Danny Levy told journalists the attacker had a criminal record. An alleged accomplice has also been arrested.

"This morning, a heinous terrorist went out, reached Kokhav Yair, and unfortunately managed, before being eliminated, to murder an Israeli citizen and injure others," Israeli Prime Minister Benjamin Netanyahu told his cabinet.

Police said they had killed the suspect after a brief chase and recovered the weapon and the car used in the attack.

A second suspect was later arrested after he "made statements suggesting involvement in the attack," the police said. They added that he had tried to attack officers.

Far-right National Security Minister Itamar Ben-Gvir said "the law on the death penalty for terrorists also applies to Israeli Arabs".

"If he had been captured, I would have demanded that he be executed. But it is better that he was eliminated beforehand," he said.

Ben-Gvir was referring to the new Israeli law to make the death penalty the default sentence for Palestinians convicted of deadly terror attacks.

About a fifth of Israelis are Arab citizens who often identify as and with Palestinians.

In the West Bank, local Palestinian sources and Palestinian official news agency Wafa reported that Israeli forces closed two checkpoints at entrances to the city of Tulkarem, located north of the scenes of the attacks.

Temporary checkpoints were also set up at the entrance to nearby Qalqilya.