Ahmed Abul Gheit, the Egyptian foreign minister, told reporters on Saturday that Hamas leaders and the Palestinian leadership were invited to Cairo.
"There is an Egyptian desire to control the border and to control the flow of Palestinians in and out of the Gaza Strip," Abul Gheit said.
Thousands of Palestinians have crossed in and out of Egypt to buy food, fuel and other necessities after Hamas fighters used bulldozers to smash through the border wall.Patience 'wearing thin'
Egyptian forces are reportedly moving to close their breached border with the Gaza Strip by stopping vehicle traffic and further tightening their security cordon around the town of Rafah.
Security guards blocked one of the gaps carved into the border wall with piles of sand and border police were stopping cars with Palestinian number plates from entering Egypt and Egyptians cars from crossing into Gaza.
Pedestrians, however, continued to move back and forth freely.
Abul Gheit said that the government's patience with the situation was running out, following the wounding of dozens of members of the Egyptian security forces. He also condemned what he called Palestinian "provocations".
Egyptian border guards were now authorised to return fire if attacked, according to a security official.
Mahmoud Abbas, the Palestinian president and Fatah leader has agreed to meet with Hosni Mubarak, the Egyptian president, to discuss the crisis, his aide said late on Saturday.
The pair will meet on Wednesday, but Abbas has already said that he plans to retake control of the Rafah border crossing and will urge Ehud Olmert, the Israeli prime minister, to accept his proposal at a planned meeting on Sunday.
Security forces loyal to Abbas were forced to leave the border crossing when Hamas seized full control of the territory in June.
Abul Gheit said that Egypt desired "to restore the arrangements which existed on the border" before June.
However, Hamas, in accepting the offer of direct diplomacy with Cairo, challenged Abbas's plan to assume control.
"We are offering an alternative, which is the operation of Rafah crossing, and we are ready to co-ordinate this with the Egyptian government," Sami Abu Zuhri, a senior Hamas official told reporters on Saturday.
Al Jazeera's Jacky Rowland, reporting from the Gaza side of the Rafah crossing, said that the Israeli blockade had failed to damage the Hamas movement.
"Many believed their credibilty would crumble in the face of so much pressure, but the border opening and the fact that Gazans can break out of this prison, is now seen to be the work of the Hamas leadership."
The two rival factions are unlikely to hold direct talks any time in the near future because of Hamas's seizure of the Gaza Strip.
Al Jazeera's Nour Odeh, reporting from the West bank town of Ramallah said: "He [Abbas] is sticking by his demands that Hamas withdraw its control of Gaza."
|Thousands of Palestinians have entered Egypt |
to collect food and other necessities [Reuters]
Amr El Kahky, Al Jazeera's correspondent on the Egyptian side of the Rafah crossing said on Saturday that indirect measures were being used to ease the influx of Gazans.
"One of these ways was to order shops to close, hotels not to host Palestinians and flat owners not to rent their flat for any Palestinians, these measures are being taken," he said.
"Almost 4,000 troops are being sent to Rafah to close and seal the city completely from outside. Every single car is checked thoroughly, no Palestinians can pass through the checkpoint in Egypt."
The Egyptian government has been heavily criticed by the US and Israel for allowing the border to remain open.
Israel tightened its blockade of the Gaza Strip last week saying the move was intended to counter cross-border rocket fire by Palestinian groups.
The closure of the territory led to dwindling supplies of food, fuel and other basic necessities in the Gaza Strip, which Hamas siezed control of in June last year.
Mubarak has called on Israel to "lift its siege" and "solve the problem".