The move followed efforts to prevent an escalation in ongoing violence that has raised fears of a new war between Israel and the Palestinian territory's Hamas.
Israel police questioning more officials in Shikun bribery probe
"The decision comes after a decrease in the violent events in Gaza over the weekend and efforts Hamas made to restrain" demonstrators, a statement from Defence Minister Avigdor Lieberman's office read.
On Wednesday, Lieberman had ordered the closure of the Kerem Shalom goods crossing and the Erez crossing for people, after a rocket from the Palestinian territory hit a home in southern Israel, prompting the Jewish state to strike 20 Hamas targets in Gaza.
Hamas disavowed the launch and said it was investigating the incident, as alarm over a potential broader conflict rose.
Near daily protests along the Gaza border since March 30 against Israel's crippling 11-year blockade of the impoverished enclave have sparked repeated clashes with the army.
More than 200 Palestinians and one Israeli have been killed in the violence.
On Friday, thousands again gathered for protests in northern Gaza, but demonstrators largely remained at least 100 metres from the border.
An Israeli army spokesperson told AFP that while most of the protesters stayed back from the fence, some came close and threw explosive devices and hand grenades at troops, while burning tyres.
At least 130 Palestinians were injured by live fire in clashes with Israeli soldiers, the Gaza health ministry said.
Hamas officials were seen discouraging protesters from nearing the fence.
Israel lets food, goods back into Gaza as Egypt pushes truce
Israel had on Wednesday also suspended the delivery of fuel for the Palestinian territory's power plant that had been trucked daily into Gaza under a deal brokered by the United Nations.
"The decision on the renewal of the fuel from Qatar has been put off as for the time being, and will be examined in a number of days based on the events," the Sunday statement from Lieberman said.
An Egyptian security delegation that visited the Gaza Strip on Thursday had encouraged Hamas leader Ismail Haniya to calm the protests, according to an Egyptian official.
On Friday, United Nations envoy Nickolay Mladenov also urged all sides "to exercise restraint, to proceed in a peaceful manner, and to avoid escalation".
Israel and Hamas have fought three wars since 2008 and fears of a fourth have spurred efforts by Egypt and the United Nations for a wider deal that would see Israel ease its blockade in exchange for a long-term truce.
Israel indefinitely postpones demolition of Bedouin West Bank village
Israeli Prime Minister Benjamin Netanyahu has frozen plans to demolish a strategically located Bedouin village in the occupied West Bank that has drawn the world's attention, his office said Sunday.
"The intention is to give a chance to the negotiations and the offers we received from different bodies, including in recent days," a statement from Netanyahu's office said about Khan al Ahmar.
Israeli authorities say the small village, located east of Jerusalem along a road leading to the Dead Sea, was built illegally, and had given resident until the beginning of October to evict themselves and demolish the structures.
The fate of Khan al Ahmar has drawn international concern, with European countries calling on Israel not to move ahead with plans to demolish it.
On Wednesday, the International Criminal Court's chief prosecutor warned that Israel's planned "evacuation by force" of the village could constitute a war crime.
The residents have refused to leave on their own, and Israel had been making the preparations to expel the residents and demolish the village.
The decision to evict the village followed years of legal battles and after negotiation attempts to agree on an alternative site for relocation failed.
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