Israel has temporarily relaxed its blockade of Gaza after hundreds of thousands of Palestinians were left without power and essential supplies.
Gaza's only power plant is now being refuelled
A spokesman said the blockade, which has provoked widespread international criticism, was being lifted for a day.
At the Rafah border crossing from Gaza into Egypt, gunfire broke out as Egyptian security forces blocked Palestinians trying to leave Gaza.
Israel had shut crossings into Gaza in response to rocket attacks from there.
Palestinian Authority President Mahmoud Abbas stressed that civilians in Gaza, which is run by militant group Hamas, were not firing the rockets into Israel.
Mr Abbas condemned such attacks as "futile launchings" that had to be stopped.
He told reporters in the West Bank town of Ramallah: "We will continue our efforts to get a total lifting of the blockade."
Shooting broke out as Palestinians trying to cross the Rafah border post - Gaza's only crossing that bypasses Israel - were confronted by Egyptian security forces.
Hundreds of protesters from the Gaza side stormed Rafah demanding the reopening of the border crossing, which has been closed for most of the time since June.
Earlier, US Secretary of State Condoleezza Rice said she had urged the Israeli government to avert a humanitarian crisis.
The UN Security Council will later discuss the situation in Gaza in an emergency session.
Israel shut its border crossing with Gaza last Thursday and lifted the blockade for one day on Tuesday, saying it would be reviewed after that.
It allowed lorries carrying industrial diesel for the coastal territory's sole power plant to entered the Nahal Oz fuel terminal.
More fuel will be delivered over the next three days along with diesel for generators, domestic cooking gas and food and medicine, the Israeli foreign ministry said.
The blockade had forced the Nusseirat power plant, which depends on fuel deliveries from Israel, to shut down on Monday, plunging Gaza City into darkness.
Israel accused Hamas of "fabricating" the power shortage, pointing out that the power plant in Gaza produces only a minority of the territory's power.
Israel said it was still providing nearly 70% of the territory's power directly.
The decision by Israeli Defence Minister Ehud Barak to ease temporarily the restrictions followed a warning from the UN that food aid to about 860,000 Gaza people could be halted within days because of the blockade.
Israel says border closures will stop if the rocket attacks end
Earlier, a warning from Israeli Prime Minister Ehud Olmert that life would not be "pleasant or comfortable" for Gazans as long as rocket attacks continued prompted UN officials to join the EU in accusing Israel of "collective punishment".
The Israeli government said its lockdown had stopped missile attacks - but another rocket struck the Israeli town of Sderot on Tuesday.
UN officials expressed relief that fuel deliveries had restarted, allowing them to provide the food aid on which some 80% of the Gazan population rely.
A spokesman for Hamas, Sami Abu Zuhri, said the crisis would remain despite the easing of border restrictions.
"The real crisis of our Palestinian people is the continuing siege on the Gaza Strip," he said.
Israel imposed an economic embargo on Gaza after the Islamist militant group seized control from the rival Fatah group in June. Israel has also limited the movement of people in and out of the territory.