Israeli Prime Minister Ehud Olmert has said he will not let his country's blockade of the Gaza Strip turn into a humanitarian crisis.
Gazans scrambled through the debris at the Rafah crossing
But he said he could not allow Gazans to live normal lives while people in southern Israel were under rocket fire.
He was speaking hours after tens of thousands of Palestinians surged into Egypt to buy supplies as the border wall was partly destroyed.
Egypt has said it will not use force to send them back.
Foreign ministry spokesman Hossam Zaki said the border would be closed again when all the Palestinians had returned.
Egyptian police reinforcements moved into the area on Thursday morning.
But the BBC's Ian Pannell at the border says it would be difficult for them to stem the continuing flow of people without the assistance of the militant group Hamas, which controls the Gaza Strip.
Shells and rockets
Israel imposed the blockade last week. It was eased slightly on Tuesday to allow some fuel and medicines through, but Israel has now re-imposed the fuel restrictions.
Speaking at a security conference, Mr Olmert vowed to keep up pressure on Gaza until rocket attacks from its territory ceased.
17 January: Israel seals border following rise in rocket attacks
20 January: Gaza's only power plant to shuts down
22 January: Israel eases restrictions
22 January: Egyptian border guards disperse Palestinian protest against closure
23 January: Border wall breached
"We will not hit food supplies for children or medicines for the needy," he said.
"But there is no justification for demanding we allow residents of Gaza to live normal lives while shells and rockets are fired from their streets and courtyards at Sderot and other communities in the south."
Israel has called on Egypt to take control of the border and is concerned that weapons will be smuggled into Gaza.
"We expect the Egyptians to solve the problem," said Foreign Ministry spokesman Arye Mekel on Wednesday.
The UN Security Council is on Thursday due to meet for the second time in three days to try to agree a statement calling for an immediate end to the violence in Gaza and southern Israel.
Call for talks
On Wednesday, at least 50,000 Gazans packed into cars and donkey carts or crossed the Egyptian border on foot after parts of the wall were blown up militants.
With reports that entire families were continuing to stream into Egypt from Rafah late on Wednesday, a senior Hamas member called for the border crossing to remain open.
"We want also a window for our people, because we have sick people - they want to get treatment and medical support," Ghazi Hamad told the BBC.
Hamas leader Ismail Haniya, meanwhile, has called for urgent talks with Egypt and his rival, Palestinian Authority President Mahmoud Abbas, on border crossings.
"We demand that our Arab brethren make a clear, practical and quick decision to take all measures and procedures to practically end the Gaza Strip siege," said Mr Haniya.
The Hamas leader seemed to respond positively to an offer from Palestinian Prime Minister Salam Fayad to control Gaza's borders - so far rejected by Israel.
"We do not want to control everything, we are part of the Palestinian people," said Mr Haniya.
Mr Olmert also vowed to continue talking to Mr Abbas, who controls the West Bank. Gaza has been ruled by Islamists Hamas since June.
"There is no Palestinian leadership better than this one to negotiate peace," Mr Olmert said, adding that he intended to keep his pledge to reach a peace agreement by the end of the year.
The UN Security Council is due to meet on Thursday for the second time in three days to try to agree a statement calling for an end to the violence in Gaza and southern Israel.
Palestinians have broken through the border before, in 2005, and it was quickly resealed with barbed wire, but reports say that on this occasion two-thirds of the border wall was destroyed.
In recent months the border has been mostly sealed, in an understanding between Israel and Egypt.