Jerusalem (AFP) - Israel stepped up security nationwide Tuesday after a soldier and a settler were killed in separate Palestinian knife attacks as months of unrest in Jerusalem spread across the country.

Thousands of police deployed at potential flashpoints as Palestinians held low key ceremonies to mark 10 years since the death of their iconic leader Yasser Arafat in mysterious circumstances in a hospital near Paris.

On Monday a 17-year-old Palestinian in Tel Aviv stabbed a 20-year-old soldier who later died of his wounds in hospital. The assailant fled but was arrested.

Hours later, a Palestinian attacked three Israelis outside the Alon Shvut settlement in the southern West Bank, killing a young woman and wounding two other people before a security guard shot and critically wounded him.

The bloodshed followed months of clashes between Israeli security forces and stone-throwing Palestinians in and around annexed east Jerusalem.

The unrest spread to Arab areas of Israel at the weekend after police shot dead a young Arab-Israeli during a routine arrest operation.

With the public increasingly on edge, Israel once again boosted security measures.

"The police have been placed on an advanced state of alert. Thousands of police, officers, volunteers and reinforcements have been deployed across the country to ensure the security of the public," police spokeswoman Luba Samri told AFP.

Following the Tel Aviv attack -- carried out by a Palestinian staying in Israel without a permit -- police began a nationwide crackdown on illegals, she said.

The authorities urged the public to "be vigilant" and report "any suspicious vehicle or individual."

The growing sense of fear on the streets has evoked memories of the second deadly Palestinian intifada, or uprising, which began in 2000.

"This is the same soundtrack that we all remember from the days of the intifada: you haven't yet had time to come to terms with the morning's terror attack .. and your heart skips a beat because you know that within an hour or two there is going to be another," commentator Alex Fishman wrote in the top-selling Yediot Aharonot.

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"You've come to feel that same oppressive sense of threat to your personal safety, and everyone... begins to ask themselves: should I or shouldn't I drive into Jerusalem? Should I or shouldn't I board the bus?

"If this madness doesn't stop right now, we are going to find ourselves back in those same dark days of the second intifada."

- A slippery slope -

Overnight, police arrested five people in the southern Bedouin town of Hura for throwing stones at a police car, and found one of them -- a woman -- to be carrying an M16 assault rifle.

In annexed east Jerusalem, five cars in Beit Safafa had their tyres slashed and offensive anti-Arab graffiti was sprayed nearby. And in the western part of the city, police arrested four Jewish minors for throwing stones at a taxi for "nationalist motives."

The Israeli army also confirmed deploying reinforcements in the West Bank.

Israel has significantly increased the police presence on the streets in recent months in a bid to rein in the unrest, but has been unable to stop a growing number of attacks by lone Palestinians, most of them in Jerusalem.

Monday's violence was further afield, reaching Tel Aviv and the southern West Bank in a move strongly condemned by Washington and Brussels.

"It is absolutely critical that the parties take every possible measure to protect civilians and de-escalate tensions," said US State Department spokeswoman Jen Psaki.

Israel has been struggling to contain the growing wave of violence which has gripped annexed east Jerusalem for the past four months since the murder of a Palestinian teenager by young Jewish extremists.

It has been further fuelled by tensions at the flashpoint Al-Aqsa mosque compound, as well as by moves to expand the settler presence in the occupied eastern sector of the city.

Since August, Jerusalem has seen four Palestinian attacks -- three "hit-and-run terror attacks" which killed five Israelis and one attempted drive-by shooting.

All four perpetrators, who acted alone and came from east Jerusalem, were shot dead, sparking further unrest.

Since July, Jerusalem police have arrested some 900 Palestinians for public order offences and indicted around a third of them.

The unrest spread at the weekend after police shot dead a 22-year-old Arab-Israeli in Kufr Kana near the northern city of Nazareth, triggering a wave of rioting in Arab areas.