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The two sides discussed "the efforts exerted by Egypt to shore up the Gaza ceasefire, end the blockade on Gaza and resume the Palestinian national dialogue," reported the Egyptian MENA news agency.
No more details of the closed-door talks, three days after an Israeli official's visit to Cairo on the Gaza issue, are available at the moment.
Egypt has invited Israel and Hamas to hold separate meetings in Cairo on means of consolidating a ceasefire in the Palestinian enclave.
On Thursday, Amos Gilad, head of the Diplomatic-Security Bureau of Israeli Defense Ministry, discussed with Suleiman the measures to stop arms smuggling via the tunnel-ridden Egypt-Gaza border.
Israeli Prime Minister Ehud Olmert declared late on Jan. 17 a unilateral ceasefire in the Hamas-ruled Gaza Strip, after a 22-daywar which claimed more than 1,300 lives.
Hamas and other Gazan militant groups later echoed that they would stage a one-week ceasefire with Israel, leaving room for further negotiations under the auspices of Egypt.
Meanwhile, Egyptian mediators will carry out talks with various Palestinian factions as of Sunday for a lasting truce in Gaza and inter-Palestinian reconciliation, according to MENA,
Representatives of the Palestine Liberation Organization (PLO) factions, including Fatah, the Palestine Democratic Union, the Palestinian Arab Front and other factions, will arrives in Cairo later on Sunday.
In addition, teams of the Democratic Front for the Liberation of Palestine (DFLP) and the Popular Front for the Liberation of Palestine (PFLP) are set to arrive in Egypt on Jan. 26, said MENA.