The Israelis have temporarily opened the Karem Abu Salem border crossing with Gaza to allow a limited supply of humanitarian aid to reach the territory.
Thirty trucks, 11 of which are carrying United Nations (UN) supplies, were allowed to travel into the Strip on Monday.
Ayman Mohyeldin, Al Jazeera's correspondent in Gaza, said: "One UN official told me ... there will be enough to last a week, but in a week's time, if Gaza doesn't get more supplies, the UN will be in the same position."
Mohyeldin reported that UN officials had likened allowing limited supplies through to "a sort of drip-feeding" of the territory.
Israel stepped up its blockade of Gaza - keeping crossings closed and so preventing the delivery of fuel and essential humantarian supplies - in response to Palestinian fighters launching rockets into southern Israel.
Power plant closed
The Israelis have almost continuously enforced the blockade since November 5, halting the supply of UN food and medical aid to 750,000 Palestinians and forcing the territory's sole power plant to shut down.
Our correspondent said the Israeli government had been clear that border crossings would remain closed while rockets attacks continued.
However, Palestinians say the policy is one of collective punishment and ignores Israel's humanitarian responsibilities in ensuring civilians receive adequate food and medical supplies.
Mohyeldin said there had been rumours that Israel was seeking to transfer those responsibilities to another border country - possibly Egypt.
As relations between Israel and Gaza sink even lower, Ehud Olmert, Israel's outgoing prime minister, has declared the five-month truce with Hamas in the Gaza Strip "shattered" following 13 days of tit-for-tat attacks.
Olmert told an Israeli cabinet meeting on Sunday that he had ordered security chiefs to draw up plans to end rocket and mortar attacks on southern Israel, the news agency AFP reported.
Olmert made the remarks shortly after four Palestinian fighters from the Popular Resistance Committees were killed in an Israeli air attack in northern Gaza.
Israel said the air raid had targeted Palestinian fighters who were preparing to launch rockets. Scores of rockets have landed in the south of the country in the last two weeks.
Nevertheless, a day later Olmert promised to release 250 Palestinian prisoners in December, in a goodwill gesture to the leadership of Mahmoud Abbas, the Palestinian president.
"Prime Minister Olmert told the Palestinian president that Israel will release 250 Fatah-aligned prisoners on the occasion of the upcoming holiday Eid al-Adha," David Baker, an Israeli government spokesman, said.
The prisoner issue is extremely sensitive in Palestinian society.
Israel holds more than 9,000 prisoners, and nearly every Palestinians has a relative, friend or neighbour who has served time.