The Palestinian deployment on Friday is part of new Palestinian President Mahmud Abbas' plan to halt violence and revive peace talks.
Palestinian security sources said about 2000 paramilitary police were assigned to border towns Bait Hanun and Bait Lahya and other parts of northern Gaza to prevent resistance fighters firing rockets and mortars at Jewish settlements and Israel.
Aides to Abbas said he had discussed with resistance leaders in Gaza this week the need for restraint to help ensure Israel pulls Jewish settlers out of the territory this year as planned - a step Israel says it will not take "under fire".
"Our orders are clear: to control these areas and to stop attacks," said Ismail al-Dahduh, a senior Palestinian officer, after briefing a group of 100 security personnel.
But asked what would happen if his men encountered fighters on a mission to attack Israelis, Dahduh said: "We will avoid clashing with them and we will talk to them in a positive way."
In what could be an initial sign of progress in Abbas' efforts to achieve calm, no mortars or rockets have been fired in Gaza since Tuesday.
West Bank raid
Shirin Abu Akla, Aljazeera correspondent in Ram Allah, said Israeli occupation forces backed by military vehicles entered the city's centre after midnight on Thursday.
The forces were deployed outside the Palestinian presidential headquarters and besieged one of the buildings where explosions were heard.
Palestinian sources said the Israeli forces detained the father, mother and an uncle of a wanted Palestinian. But unofficial Israeli sources said seven Palestinians were arrested.
Israel has partially reopened Gaza's Rafah crossing with Egypt, which was closed in December when resistance fighters bombed an army post at the terminal, killing five soldiers.
Hiba Akila, Aljazeera's correspondent in Rafah, said the crossing has been reopened and the first bus carrying passengers has crossed the border heading for the Palestinian territories.
Israel closed the Rafah crossing
after an army post was bombed
The crossing has only been opened to Palestinians who have been stranded at the Egyptian side and Hajjis (pilgrims) who are expected to return within the coming days.
The crossing is not open to people hoping to use Egypt as a stopping place before travelling abroad.
The crossing will be open until 8pm every night for the next few days as 20,000 stranded Palestinians make their way home.