The Israeli defence ministry closed the crossings last week after Palestinian fighters fired rockets into southern Israel.
Late on Monday, Ehud Barak, the Israeli defence minister, revised his decision to keep the crossing completely sealed and authorised a "limited resumption" of supplies to the Gaza Strip.
The partial resumption of fuel shipments, expected to begin on Tuesday at 06:00 GMT, followed a request by Tony Blair, former UK prime minister and envoy of the Middle East Quartet - comprising the European Union, the US, Russia and the United Nations.
"The fuel supply will be resumed completely when rocket fire from the Gaza Strip has ceased," Barak said.
Hospital fuel fears
"Some of the smaller hospitals will start running out of fuel in the next 36 hours"
Al Jazeera's correspondent in Gaza
Aside from general supply problems, Tadros highlighted two areas of serious concern following the cut in power.
"The electricity supply affects the water pumps that deal with the sewage system here, and electricity is needed for hospitals," she said.
"Some of the smaller hospitals will start to running out of fuel in the next 36 hours - that's going to be the immediate concern."
However, Israel insisted the Strip was getting enough electricity from the Israeli and Egyptian grids to meet 75 per cent of demand. The foreign ministry accused Hamas of exploiting the situation for political gain.
"The cynical Hamas exploitation of the civilian population in Gaza is contemptible," a ministry statement said.
The European Commission, which funds fuel deliveries to Gaza's sole power plant, said it had been informed that the Israelis may authorise fuel shipments on Tuesday.
"The Israel liaison office with the Palestininan territories told us that the deliveries to the power station could resume tomorrow," an European Union spokeswoman said.
Israeli sources said, on condition of anonymity, that shipments would resume if no more rockets are fired into southern Israel.
|Gazans have been using blackmarket fuel smuggled into the territory to get by [AFP]
Kanan Obeid, a Gazan energy official, criticised the move as an example of "Israel's policy of collective punishment".
The Gaza City plant provides about a quarter of Gaza's electricity, while most of the rest comes over lines from Israel. Egypt also provides a small amount.
A network of tunnels linking Gaza to Egypt is known to be used by Gazans to bypass Israel's blockade of the territory and bring products - including some fuel - into the Strip.
Ayman Mohyeldin, reporting for Al Jazeera from Gaza, said while the trickle of unofficial supplies has enabled individuals to get by, it cannot be used to power "the critical infrastructure of Gaza".
"There's two reasons for that - the Egyptian quality of petrol isn't high enough to power the generator, but at the same time the generator is monitored by EU observers and they will not allow any blackmarket fuel to be used to generate electricity for Gazans," he said.
Peter Lerner, the co-ordinator of Israeli activities in the Palestinian territories, said: "We received a request [from the Palestinians] for deliveries of fuel to resume and we forwarded the request to the defence ministry in Tel Aviv."
Most of the fuel and gas supplies needed by the Gaza Strip usually goes through the Nahal Oz terminal between Israel and the Palestinian territory.
Press freedom 'violated'
The crossing closure has also prevented journalists from entering the strip for five days, something that has drawn protests from the Tel Aviv-based Foreign Press Association (FPA).
The FPA, which represents foreign reporters in Israel and the Palestinian territories, branded the Israeli-imposed restriction as "a serious violation of press freedom".
Israel repeatedly closes the crossings into Gaza, derailing the Gazan economy and putting the territory's citizens under pressure, in response to rockets fired from the Strip by Palestinian fighters.
Even as the crossings were closed, there were fresh calls for the largely stagnant peace process between the Israelis and the Palestinians to be revived.
The Middle East Quartet - which groups the EU, Russia, the UN and the US - held a meeting in Egypt on Sunday and called for peace talks to be carried forward.