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Both sides hailed the meeting, to discuss the Israeli blockade of Gaza, as a "turning point" in relations.
Hamas' leader in the Gaza Strip Ismail Haniya has met with Egypt's Islamist President Mohamed Mursi, with both sides hailing it as a "turning point" in relations.
Mursi and Haniya reportedly discussed ways to ease Israel's blockade on Gaza, including the movement of Palestinians into Egypt, Haaretz reported.
Meanwhile, a Palestinian official told Tunis Afrique Presse that the head of Egyptian intelligence had promised an increased flow of Qatari fuel to Gaza via Egypt, to help ease power shortages in the strip.
Egypt announced the opening of its border with Gaza after President Hosni Mubarak was deposed in February 2011.
Mursi's Muslim Brotherhood party was viewed with suspicion by Mubarak. Hamas is an offshoot of Muslim Brotherhood.
Gaza has been under semi-blockade by Israel and Egypt since Hamas took routed Fatah in 2007 elections, according to Agence France-Presse.
Mubarak eased the blockade in 2010, but did not allow commercial traffic through the Rafah border crossing as Hamas had hoped.
Hamas hoped Mursi’s victory would strengthen its position.
However, while Egypt had eased visa requirements for Gazans under 40 crossing the border, "severe restrictions" had remained in place, Haaretz wrote.
And Tunis Afrique Presse wrote that Cairo was unlikely to be ready to open up its border with Gaza to the extent sought by Hamas, mainly due to the influence still wielded by the Mubarak-era security establishment.
AFP reported that Haniya’s visit to Cairo was the second by a top-ranking Hamas official since Mursi’s election last month.
Mursi has been conducting a number of high-profile meetings, including last week with Palestinian President Mahmoud Abbas, of the rival Fatah movement that governs the Israeli-occupied West Bank.
"The meeting between [Haniya and Mursi] constitutes a real turning point in bilateral relations," Haniya's spokesman in Gaza, Taher al-Nunu, said in a statement.
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