The handover marks the first stage in a trial agreement which could see further Israeli withdrawals from the West Bank and Gaza Strip in exchange for efforts by the Palestinian Authority to quell anti-Israel attacks.

We want the people to go back to their regular lives and to live in peace

Mohammed Fatahah Palestinian policeman

But as the troops were pulling out of Bethlehem in the south, other Israeli forces entered the Tulkarm refugee camp in the northern West Bank sparking an exchange of fire in which at least one Palestinian gunman was killed.

And two people have been killed in the southern Gaza Strip: an Israeli soldier by sniper fire and a Palestinian teenager shot by Israeli troops posted outside a settlement.

So far there has been no sign of Israel implementing its pledge to redeploy troops in the Gaza Strip.

Jewish settlers in Gaza have protested strongly to the government about the deal, saying it would threaten their security.

'Encouraging step'

Palestinian leader Yasser Arafat has agreed to launch a crackdown on militants - although the deal has already been rejected by key Palestinian factions.

"We want the people to go back to their regular lives and to live in peace," said one Palestinian policeman, Mohammed Fatahah, just before setting out on patrol in Bethlehem.

The agreement was struck on Sunday

The Israeli army has said it intends to maintain a presence around Bethlehem - at least until Palestinian security forces take full control.

BBC correspondent James Reynolds, who is in Bethlehem, says there is no great celebration in the town because many people are sceptical that the deal will last.

But the United States has welcomed developments, saying the agreement was an "encouraging" step towards resuming other peacemaking moves.

Our correspondent says diplomats are working hard to sustain the agreement, but an event such as a suicide bombing could quickly undermine their efforts.

Israel has said it will carry on with military action wherever necessary to protect its security.

New violence

Israeli troops in more than 50 tanks, jeeps and armoured personnel carriers entered the Tulkarm camp on Tuesday and conducted house-to-house searches.

Hamas and the Palestinian people reject any agreement which aims at destroying our resistance and ending the intifada

Hamas statement

Military sources reported initially that two Palestinian fighters had been killed in an exchange of fire, but later said one had died and the other was wounded.

Army radio said 15 people were detained for questioning in Tulkarm, which has been under almost constant curfew in recent weeks.

The army says it was acting on a warning that Palestinian militants there were planning an attack on Israeli civilians.

The bloodshed in the southern Gaza Strip followed a night of sporadic gunfire directed at Jewish settlements there.

The military wing of the radical group Hamas claimed responsibility for killing the soldier in a statement faxed to news agencies.

Militant warning

The security deal, struck on Sunday, has been rejected by key Palestinian elements, including Hamas, Islamic Jihad and even from within Yasser Arafat's Fatah movement, whose members said it was a poor substitute for full Israeli withdrawal.

The confidence-building measure was reached by the Palestinians' Abdul Razak al-Yahya and Israeli Defence Minister Binyamin Ben-Eliezer at talks in Tel Aviv after several days of relative calm on the ground.

Israeli forces have been in military control of most of the Palestinian towns in the West Bank for the past two months after a wave of suicide bombings by Palestinian militants.