The deployment comes after a deal with Israel
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Palestinian security forces have begun taking up positions in the northern Gaza Strip, to prevent militants firing rockets at Israeli targets.
Up to 3,000 police officers were expected in the area including border towns Beit Lahiya and Beit Hanoun.
The deployment has led Israel to halt plans for a major ground incursion.
A 17-year-old Israeli girl, Ella Abukasis, died on Friday after being wounded in last weekend's Qassam rocket attack into the Israeli town of Sderot.
Ella Abukasis was the fifth person from Sderot to die from a Palestinian rocket attack since June last year.
Two days before last Saturday's attack six Israelis died when Palestinian militants ambushed a border crossing in Gaza.
Tension possible
The first Palestinian units started patrols on Friday after Israel accepted detailed plans submitted by Gaza security chief Musa Arafat.
Vehicles were being checked for weapons close to the Erez border crossing.
The BBC's Alan Johnston reports from Gaza that there is the potential for friction between police officers and the militants, even though both sides will be keen to avoid that.
And he adds that Mr Abbas's camp is suggesting that the largest Palestinian militant group Hamas is perhaps now moving towards some kind of ceasefire arrangement.
The Rafah border from Egypt to Gaza was partially re-opened to incoming traffic on Friday.
Israel was also reported to have eased traffic restrictions on the main road running north-south through Gaza.
Mr Arafat has said the deployment will be extended to the south of the Gaza Strip.
Reaction in Israel to the Palestinian deployment was generally positive.
Army Chief of Staff Moshe Yaalon said the move showed that Palestinian leaders "understand more and more that terrorism does not pay".
"This is an effort here that was never seen during the lifetime of Yasser Arafat," said Israel's Interior Minister, Ophir Pines.
The Palestinian troop deployment came after Israel lifted a ban on contacts with newly-elected Palestinian Authority President Mahmoud Abbas.
Israeli Prime Minister Ariel Sharon had accused Mr Abbas of not acting swiftly after last week's attack.
Speaking after prayers in Gaza on Thursday, where he has spent this week negotiating a possible ceasefire with militant groups, Mr Abbas said Palestinians "believe in peace, and we believe in negotiations".