An Arab gunman who shot dead three Israelis in Tel Aviv last week has been killed in a shootout with police, following a massive manhunt that put Israelis on edge while the killer was on the loose.

The gunman "was found in a building" today, police spokeswoman Luba Samri said.

He came out shooting at the special forces and "was then shot and killed", she added.

The gunman was identified earlier as Nashat Milhem, an Arab from northern Israel.

He opened fire at a bar on a busy street in Tel Aviv last Friday, killing two people and wounding several others. He later also shot and killed an Arab taxi driver.

The incident came amid more than three months of near-daily Palestinian attacks against Israeli civilians and soldiers.

Ms Samri said Milhem had opened fire at the police with the same gun he used in the attacks in Tel Aviv.

Milhem was found near the Arab village of Arara in northern Israel where he is from, police said.

Hakim Younis told Channel 10 TV that he witnessed some of the incident from his home.

"I was sitting on my balcony with my cousin ... when suddenly shooting began, hundreds of bullets, like in a war," Mr Younis said, adding that he then went inside and did not see anything further.

Israelis are used to quickly resuming their daily routines following attacks because assailants are usually swiftly captured or killed. But the Tel Aviv shootings left Israelis jittery because Milhem, who was considered armed and dangerous, was on the loose for a week.

Milhelm's relatives had said he was "traumatised" after a cousin was shot dead in a 2006 police arrest raid. At the time, police said they were searching for weapons and claimed the shooting was in self-defence.

Milhelm served time in an Israeli prison after being convicted of attacking a soldier and trying to steal his weapon. But he was also described by residents of the upscale Tel Aviv neighbourhood where he worked as a grocery shop delivery man as being well-liked and trusted.

Israeli Arabs, who make up a fifth of the country's 8.4 million people, enjoy full rights but have long complained of unfair treatment in areas such as housing and employment opportunities. Many identify more with their Palestinian brethren in the West Bank and Gaza and with Palestinian nationalism rather than with Israel.

The near-daily Palestinian attacks on Israeli civilians and soldiers have killed 21 Israelis, mostly in stabbings, shootings and car-ramming assaults. At least 134 Palestinians died by Israeli fire, including 93 said by Israel to be attackers. The rest were killed in clashes with troops. These figures do not include Milhelm's victims.