Angry protesters 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."
Egypt called on Hamas to urge residents of the Gaza Strip to avoid further unrest.
Hossam Zaki, the foreign ministry spokesman, expressed Egypt's "deep regret at the events witnessed at the Rafah border crossing".
Egypt "asks those in control of the Gaza Strip to work to avoid the repetition of such a situation", he said.
At least four Palestinians were wounded during the protest, medics said.
Eleven Egyptian policemen were injured, including one from gunfire and the other 10 from rocks thrown at them.
Meanwhile, amid mounting international fears of a humanitarian crisis, 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 morning.
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.
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
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, lights were back in most of Gaza City by Tuesday afternoon.
Israeli tanker lorries brought in 700,000 litres of fuel, enough to provide electricity to Gaza City for two days.
Mahmoud Abbas, the Palestinian president, however, called on Israel to fully lift the blockade, calling a partial easing of the lockdown "insufficient".
"This is insufficient and we will continue our efforts to get a total lifting of the blockade," Abbas told reporters in the West Bank town of Ramallah.
Abbas also renewed his criticism of rocket fire against Israel from Gaza.
"It is not the people who fire these rockets," Abbas said. "We have condemned these futile launchings in the past and we continue to do so. They must stop."
But Khaled Meshaal, the Hamas leader based in Damascus, said the rocket fire would continue as long as Israel continues its "onslaught" on Gaza and the West Bank.
"Let Israel stop its aggression and its occupation of Palestinian land and the resistance, including rockets, will stop," he said in an interview.
The impact of the blockade, which has left homes in the dark, affected hospitals and caused sewage to flood the streets, has sparked international condemnation.
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 settlers, out of 23,000, have fled Sderot because of the near-daily attacks
The main impact of the rockets is psychological torment
The Iraqi parliament unanimously condemned Israeli raids and its siege of the Gaza Strip on Tuesday.
The parliament approved a draft law to provide Gazans with aid, including food, medicine and oil in co-ordination with the Arab League and the United Nations.
On Monday, the European Union accused Israel of carrying out "collective punishment" of Gaza's civilian population.
Kyriacos Triantaphyllides, a European parliament member, told Al Jazeera: "What is happening there [in Gaza] is a major catastrophe on very big scale and it is not enough just to lift the blockade for a little while.
"I think the action of Israel against Gaza, which constitutes collective punishment for the whole people of Gaza, is to be deplored by the international community. We do not agree with this kind of measures.
Sparring at UN
Israeli and Palestinian envoys meanwhile traded accusations in the UN Security Council as the 15-nation body met to discuss the Gaza crisis.
Riyad Mansour, the permanent Palestinian observer to the United Nations, described the situation as "absolutely untenable".
"The Israeli policy of brinkmanship is creating a humanitarian catastrophe in the Gaza Strip, heightening fears and tensions, inciting, provoking and fuelling the vicious and dreaded cycle of violence," he said.
Gilad Cohen, the Israeli envoy, rejected Mansour's accusation that Israel was acting in violation of international law.
"It is the duty of all states to ensure the right to life and safety of its people, especially from vicious acts of violence and terrorism," Cohen told the council.
Source: Al Jazeera and agencies