The Palestinian Authority and Islamist movement Hamas reached an agreement to reconcile after a decade of mistrust, but offered few details on security arrangements in the Gaza Strip that had been key to negotiations.
Fatah officials said the two sides agreed that the Palestinian Authority would take over responsibility for Gaza's border crossings no later than November 1 and that full governing responsibilities would be handed over to the Palestinian Authority by the beginning of December.
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Abbas has tried numerous times without success to fix the rift, in part to counter Israeli assertions that peace negotiations are pointless because he can't ensure that any treaty will also hold in Gaza.
An Egyptian source close to the talks said intelligence chief Khaled Fawzi had followed the negotiations closely.
Fatah's Palestinian Authority President Mahmoud Abbas told reporters that he welcomed the agreement.
A split between Palestine's two major forces, Fatah and Hamas, occurred after the parliamentary elections in Palestine in 2006 when Hamas won. Hamas and Israel fought three devastating wars over the past decade.
The readout of the Secretary-General's phone call comes as media outlets are reporting that Egyptian-facilitated talks in Cairo have led to a breakthrough in the talks among Palestinian parties on administration in the Gaza Strip. "Unity and national reconciliation among the Palestinian people are our strategic option for moving forward".
Attempts at reconciliation in recent years fell apart.
Struggling with the fallout from the border blockade, Hamas has found it increasingly hard to govern or provide basic services, such as electricity, to Gaza's people.
Reconciliation could also pose a dilemma for global efforts to reach an Israeli-Palestinian peace deal since Hamas has not recognised Israel, unlike the Abbas-led Palestine Liberation Organisation.