Egypt has pressed ahead with efforts to repair sections of its border with Gaza which were destroyed by Palestinian militants a week ago.
Egypt wants to restore shared control of the border
Hundreds of thousands of Palestinians have been crossing freely into Egypt to buy essential supplies.
Barbed wire has been put in place to seal some of the breaches and riot police have been deployed.
Cairo has said it wants to work with the Palestinian Authority to agree on control of the crossing.
Palestinians were continuing to cross into Egypt on Tuesday but correspondents said that the numbers appeared to be falling.
Hamas security guards have been preventing some cars from crossing from Gaza, while Palestinians who had crossed were being sent back by Egyptian security services.
Reports said that shops in Rafah were almost empty because of Egyptian efforts to prevent new supplies from reaching the city.
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Safwat Hammad, a shopkeeper in Rafah, told the Associated Press news agency he had restocked his shop twice but was running out of produce.
"I have nothing else to sell. God forbid, they will also buy the air, and we will not be able to breathe," he said.
Egyptian President Hosni Mubarak is due to hold separate talks on Wednesday with the President of the Palestinian Authority Mahmoud Abbas and with Hamas, the radical Palestinian group which controls Gaza.
Egypt wants the Palestinian Authority to control the crossing but rival faction Hamas insists it should have some degree of control.
A senior Israeli official told French news agency AFP that if Mr Mubarak and Mr Abbas reached an understanding on shared control of the crossing, "Israel will certainly not oppose such an arrangement".
The border was destroyed by Hamas militants after an Israeli blockade of Gaza led to a shortage of food, fuel and other vital supplies.
Israel said the blockade was aimed at preventing rocket attacks by Palestinian militants on its settlements near the border.