Egypt has said it will not use force to send back Palestinians who crossed from the Gaza Strip in large numbers after parts of the border were breached.
Foreign ministry spokesman Hossam Zaki said the border would be closed again when all the Palestinians had returned.
Tens of thousands have surged in to buy food and other supplies made scarce by an Israeli blockade - aimed at stopping rocket attacks from Gaza.
Israeli PM Ehud Olmert said he would not let a humanitarian crisis develop.
"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."
Meanwhile about 15 Israeli tanks and armoured vehicles were seen in northern Gaza.
Israel confirmed that there had been "routine activity to stop terror" in the area.
The blockade imposed last week eased slightly on Tuesday to allow some fuel and medicines through, but Israel has now reimposed the fuel restrictions.
Israel and the US have expressed concern about the events at the Egyptian border, and Israel fears weapons could be smuggled into Gaza.
Mr Zaki said Egypt was trying to contain the situation but had "great understanding" of the people of Gaza and their need for basic supplies.
People had packed into cars and donkey carts or crossed the border on foot when it was breached.
With reports that entire families were continuing to stream into Egypt from Rafah as darkness fell 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.
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
Hamas leader Ismail Haniya, meanwhile, has called for urgent talks with Egypt and his Palestinian rival, 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.
Earlier, the Hamas leader seemed to respond positively to an offer from Palestinian Authority 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.
Hamas has controlled Gaza since last June.
Earlier Egyptian President Hosni Mubarak said he had let the Gazans in.
He said he had told his troops to "let them come to eat and buy food and go back, as long as they are not carrying weapons".
The BBC's Heba Saleh in Cairo says Egypt has little choice but to welcome the influx, as there is deep public sympathy for the Palestinians.
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It is good that Egypt is allowing the Palestinians through
Egypt can only hope Israel will ease its restrictions, she adds.
A total of 350,000 Gazans crossed the Egyptian border, Israel's Haaretz newspaper reported. Hamas has not taken responsibility for breaching the border but quickly moved in to police it, the paper said, confiscating seven pistols from a man returning to Gaza.
Haaretz quoted one Gazan, Mohammed Abu Ghazel, as saying he had crossed the border three times with cigarettes which he had sold for five times the price he bought them.
"This can feed my family for a month," he said.
The BBC's Tim Franks in Rafah on the Gaza-Egypt border says it will be difficult for the Egyptians to reseal the border on their own, and Hamas has very little incentive to co-operate.
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.