Palestinians have poured into the Egyptian side of the Rafah crossing through holes blown by explosions along the border wall between the Gaza Strip and Egypt.
The scenes came on the sixth day of a blockade of Gaza, imposed by Israel and backed by Egypt, in response to a spike in rocket attacks on Israeli border towns.
Later Ehud Olmert, the Israeli prime minister, said Israel would not ease its grip on Gaza.
"We will continue to strike at the leaders of terror in the Gaza Strip, even at the cost of the quality of life of its residents," he said.
"We will not prevent food for children, medication for those who need it and fuel for the instutitions that are involved in the saving of human lives.
"But there is no justification," he said, "to demand that we allow residents of the Gaza Strip to live a normal life at a time when from their streets rockets arnd shells are fired into Sderot and other communities in the south."
Mass break out
Before dawn on Wednesday, Palestinian fighters set off at least 15 explosions on the wall running through Rafah separating the two territories, Hamas security forces said.
The security forces later closed most holes, but left two open to allow the flow of human traffic.
Amr El-Kahky, Al Jazeera's correspondent, reporting from the Egyptian side of the Rafah crossing, said that Egyptian security forces did not take any action over the entry of Palestinians.
Hosni Mubarak, the Egyptian president, later said he had ordered his troops to allow Palestinians to cross into Egypt because they were starving.
"I told them to let them come in and eat and buy food and then return them later as long as they were not carrying weapons," he said.
El-Kahky said: "Those crossing over have thanked Egypt for not confronting them. Many have bought with them containers for much needed fuel.
"They have also been told by the Hamas leadership in Gaza that they should respect Egyptian security forces, get what they need, and return to Gaza."
Al Jazeera correspondent Samir Omar said all shops in Rafah were open on Wednesday morning to enable Palestinians to buy food and medicines.
Omar said quoting witnesses that some Palestinians came only to stock up on basic necessities, but others might stay back in Rafah for some time to meet their relatives stranded in the Egyptian city of Arish.
On foot, in cars or riding donkey carts, the Palestinians went on a massive shopping spree, buying cigarettes, plastic bottles of fuel, and other items that have become scarce and expensive.
Israel expressed concern that fighters and weapons might be entering Gaza amid the chaos, and said responsibility for restoring order lay with Egypt.
The previous day, dozens of Hamas protesters had stormed the Rafah crossing, demanding that the terminal be opened to ease the blockade imposed on the territory by Israel.
Several protesters were wounded as Egyptian police opened fire in the air and used batons and water cannons to push them back.
Palestinians had complained that Gaza was under siege from both Israel and neighbouring Arabs.
Um Ahmad, a Palestinian woman demonstrating at the Rafah crossing, told Al Jazeera: "The Arabs should be united with us and not against us.
"This is an appeal to all the Arabs. They should help us lift the blockade, they should stand with us."
Talks to continue
Mahmoud Abbas, the Palestinian president, said on Tuesday that he would not pull out of peace talks with Israel because of the Gaza situation.
"Halting contacts with Israel is useless," he said in his first comment since the latest round of Israel-Hamas fighting erupted last week.
Israel normally supplies 60 per cent of the electricity for Gaza's 1.5 million inhabitants
Gaza needs around 240 megawatt of electricity, but normally receives only about 200 megawatts, with 8 per cent from Egypt
Israel is the only source of industrial fuel for Gaza's power station
Israel stopped supplying industrial fuel supplies to Gaza on January 19
The EU pays Israel around $10m per month for Gaza's industrial fuel
"On the contrary, we should intensify our contacts and our meetings to stop the suffering of our people."
Abbas also renewed his criticism of rocket fire against Israel from Gaza.
He said: "It is not the people who fire these rockets. We have condemned these futile launchings in the past and we continue to do so. They must stop."
For her part, Condoleezza Rice, the US secretary of state, said on Tuesday that US officials had spoken to their Israeli counterparts "about the importance of not allowing a humanitarian crisis to unfold".
Israeli officials were receptive, she said.
Rice blames Hamas for the situation in Gaza.
Arye Mekel, a spokesman for Israel's foreign ministry, pledged that the humanitarian shipments would go on.
"We will continue [on Wednesday] and the coming days to deliver more aid to Gaza until all promised supplies get across," he said.
On the ground, two lorries carrying cooking gas and three with diesel for generators passed through Israel's Nahal Oz border crossing, east of Gaza City, early on Tuesday.
Palestinian rockets are crude homemade weapons fired by Hamas and other fighters from Gaza into Israel, with a maximum range of 10km
The rockets have killed 10 Israelis since 2005, while more than 700 Palestinians have died in Israeli raids over the same period
Rocket attacks have increased sharply since April 2006
Between 2,500-3,000 residents, out of 23,000, have fled Sderot because of the near-daily attacks
The main impact of the rockets is psychological torment
It marked the first time supplies had entered Gaza since late on Thursday, when Ehud Barak, the Israeli defence minister, ordered the territory sealed off in response to rocket fire.
Gaza City was plunged into darkness after its only power plant was shut down on Sunday, as fuel supplies dried up under the Israeli blockade.
But with Israel allowing limited supply, electricity was back in most of Gaza City by Tuesday afternoon.
Israeli tankers brought in 700,000 litres of fuel, enough to provide electricity to Gaza City for two days.
The Israeli defence ministry ruled late on Tuesday that 250,000 litres of diesel fuel could be transferred into Gaza daily.
However, the crossings would remain closed to other goods and people until further notice.
Israel has maintained all along that Hamas created an artificial crisis.