Israel's army chief on Friday ordered troops to halt operations in the Gaza Strip and to scale them back in the West Bank.
The army chief, Lt. Gen. Moshe Yaalon, also said crossings into the Gaza Strip will be opened next week.
In other developments:
Yaalon's pullback orders came just hours after some 2,000 Palestinian police completed their deployment in Gaza, taking up positions in the central and southern areas to prevent attacks on Israeli targets.
"It is in our interest to allow the Palestinians to deploy security forces throughout the Gaza Strip," a security official told The Jerusalem Post. "However, the steps must be fully coordinated with us in order to avoid accidents that could threaten the stability."
Many of the uniformed men fanned out in the Rafah area, one of the hottest flashpoints of fighting between Israeli troops and Palestinian militants. Palestinian police moved in to northern Gaza a week ago, and since then violence has dropped off sharply, reports CBS News Correspondent Robert Berger.
"Look, we have an army and we didn't even know it," a Palestinian youth from the Khan Younis refugee camp shouted as a convoy of armed Palestinian policemen went through Friday.
Palestinians lined the streets to watch the police convoy of jeeps and buses, a day after the new Palestinian leadership banned civilians from carrying weapons.
In the West Bank, Israeli forces are expected to start pulling back from towns in coming days and to begin removing some roadblocks, as part of a handover of security control to the Palestinians.
The easing of tensions came after Palestinian leader Mahmoud Abbas won a promise from armed groups that they would halt attacks if Israel stops military operations in the West Bank and Gaza.
Yaalon on Friday ordered a halt to military activity in areas of Gaza where Palestinian police are deployed. Israeli troops still maintain positions in the strip, along main roads and near Jewish settlements.
The army chief also said arrest raids in the West Bank must be minimized and will require his personal approval.
Next week, the three major Gaza crossings — Karni, Erez and Rafah — will open to Palestinian travelers and cargo. The crossings had been closed in response to attacks by Palestinian militants.
The pro-government Egyptian newspaper Al-Ahram reported that an Egyptian security team is due to travel Tuesday to meet with factions and militant groups in the Palestinian territories.
Another meeting between exiled Palestinian groups and regional leaders is expected to take place in Egypt in early February, the semi-official daily, Al-Akhar, reported Friday.
Egypt's Intelligence chief Omar Suleiman and Amos Gilad, a senior Israeli Defense ministry official, met in Egypt on Wednesday to finalize deployment details for Egyptian border police during the expected Israeli withdrawal from Gaza, according to the two dailies.
The deployment is expected next month after the two foreign ministries sign changes to the Camp David agreement, Al-Akhbar reported.
The troop move would require changes in the 1979 Camp David peace accord, which limits the Egyptian military presence along the border. In December an agreement was reached to deploy 750 Egyptian troops ahead of the withdrawal.
David Satterfield, a senior State Department Middle East expert, said Thursday the prospects for movement in the Arab-Israeli conflict were better than at any time over the past four years.
Addressing a conference sponsored by the U.S. Institute of Peace, Satterfield said the Gaza withdrawal that Israel has proposed offers a "tremendous opportunity" for progress toward a peaceful settlement.
He cautioned, however, that a Palestinian state "can't be built on the foundation of terrorist violence."
Satterfield said there has been some progress in U.S. consultations with Israel on the routing of the separation barrier that Israel is constructing in the West Bank to enhance its security by screening out Palestinian bombers.