Israel has praised the Palestinian Authority after its security forces began deploying in northern Gaza to prevent militants firing rockets.
Palestinians are trying to stop rocket attacks for the first time
Israeli Deputy Prime Minister Shimon Peres said the measure, ordered by newly-elected Palestinian leader Mahmoud Abbas, was "really impressive".
Up to 3,000 Palestinian personnel have taken up positions and begun inspecting vehicles heading for Israeli areas.
Meanwhile, Mr Abbas has begun a fresh round of talks with militants in Gaza.
He has been meeting both the Hamas and Islamic Jihad groups, with some signs that the talks are making progress.
Mr Abbas argues that the only way to bring the violence to an end is to persuade the militants to agree to a ceasefire, the BBC's Alan Johnston in Gaza says.
It is two days since the last rocket attack on Israel, our correspondent adds, the longest period of calm in Gaza for many months.
Israel has threatened a major offensive in the Gaza Strip if rocket attacks continue.
On Friday, a 17-year-old Israeli girl injured in a rocket attack on the Israeli border town of Sderot last Saturday died from her injuries.
Thousands of armed Palestinian officers in dark uniforms and red berets began patrolling the border towns of Beit Lahiya and Beit Hanoun on Friday for the first time since the Palestinian intifada (uprising) began four years ago.
Some could be seen inspecting vehicles at checkpoints near the main Erez border crossing, and by the Karni crossing further south, an AFP news agency correspondent reported.
A statement from Mr Abbas' office said more personnel would be deployed further south in the next 48 hours.
Mr Peres said: "The first steps by Abu Mazen [Mahmoud Abbas] are really impressive, not only in what he has been saying but also with the actions on the ground."
Israeli Chief of Staff Moshe Yaalon said Israel was "witnessing the beginning of positive developments in the Palestinian camp, an expression of their understanding that terror does not pay."
The apparent new mood of optimism came days after Israel temporarily severed contacts with the Palestinian Authority following the deaths of six Israelis, who were killed in an ambush at the Karni crossing last week.
Senior Palestinian officer Ismail al-Dahdouh told Reuters news agency that the security forces' orders "are clear: to control these areas and to stop attacks".
But, when asked what his personnel would do if they encountered militants preparing attacks, Mr Dahdouh said: "We will avoid clashing with them and we will talk to them in a positive way."
In a goodwill gesture, Israel reopened the Rafah border crossing between Gaza and Egypt on Friday, closed since a deadly attack there six weeks ago, and eased traffic restrictions on the main north-south road in Gaza.