Mr Marzuka said Egypt's contact with Palestinians in Gaza should be through the Rafah crossing.
The Rafah crossing has been closed since 2007, although special medical cases are occasionally allowed through.
Correction 7 January 2013: This story has been amended to clarify the reference to Egypt's closure of the Rafah crossing.
The Rafah crossing disturbance involved 100 policemen, who staged a sit-in within the terminal to protest the shooting death of a policeman Thursday.
They've gotten some surveillance cameras, I guess, at the Rafah crossing.
Early on Tuesday he was taken to the Rafah crossing between Gaza and Egypt, and handed over to Egyptian mediators by Hamas, in the presence of Israeli representatives.
BBC: Gilad Shalit freed in Israeli-Palestinian prisoner swap
The Rafah crossing was open sporadically between June and January, when Egypt ordered it opened to those in need of medical care, students, and foreign passport and residency card holders.
Such has been the experience, for example, with United Nations forces in southern Lebanon, European Union monitors who were deployed for a time at the Rafah crossing between Egypt and Gaza and even U.S.-led multinational forces deployed to monitor the demilitarization of the Sinai.
Officials in Egypt long maintained that they shut their Rafah crossing with Gaza (where, incidentally Sgt Shalit was freed this morning) on the request of the PLO, which blamed Hamas for killing large numbers of supporters from President Mahmoud Abbas' Fatah party during their takeover.
During Sunday's Cabinet meeting, Barak too voiced optimism that Egypt would regain control of the Rafah border crossing.
As the search for any remaining gunmen continues, Egypt has closed its Rafah border crossing with Gaza, our Cairo correspondent Yolande Knell reports.
And on Friday it partially reopened the Rafah border crossing between Gaza and Egypt, which had been closed since an attack in early December.
Meanwhile, at the Gaza-Egypt border, nearly 25 trucks carrying aid and medical supplies were unable to pass through the Rafah border crossing on Sunday, CNN's Karl Penhaul reported.
Egypt's military leadership, the Supreme Council of the Armed Forces, said 35 assailants -- terrorist factions from Gaza -- were involved in Sunday's attack near the Rafah border crossing.
Jabari therefore shocked many observers when he appeared on television personally escorting Sgt Shalit to the Rafah border crossing with Egypt in October 2011, after a prisoner exchange was agreed between Hamas and Israel.
More than a dozen Egyptian soldiers were killed and seven others were wounded in an August 5 attack near the Rafah border crossing, when assailants with semiautomatic weapons and hand grenades stole two armored vehicles from Egyptian forces and tried to enter Israel.
The raid comes a week after 16 Egyptian soldiers were killed and seven others were wounded in an attack near the Rafah border crossing, when assailants with semiautomatic weapons and hand grenades stole two armored vehicles from Egyptian forces and tried to enter Israel.
Rafah is the crossing point on the border between Egypt and Gaza.
This will be through an international crossing at Rafah, whose target opening date is November 25th.
After Israel's withdrawal in 2005, an EU team monitored the crossing at Rafah, on Gaza's southern border with Egypt.
At the start, America tried to keep the gates open, brokering an Agreement on Movement and Access with Israel to allow the export from Gaza of hundreds of trucks of produce a day, regular bus convoys to and from the West Bank and the opening of a Palestinian-controlled crossing at Rafah to Egypt.
Israel, meanwhile, has remained notably silent about Egypt's decision last week to open the crossing between Gaza and Sinai at Rafah and its follow-up announcement on June 7th that the border would remain open indefinitely.
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