"It is just not enough," Christopher Gunness, a UNRWA spokesman said, estimating that Gazans need at least 15 lorries worth of UN supplies daily to get by.
Around 45 lorries of goods were allowed through the Kerem Shalom crossing on Monday, including 10 United Nations vehicles carrying food and medical supplies.
Around 15 truckloads of supplies were allowed through the Karni crossing with an unspecified number also passing via the Nahal Ouz crossing.
Sherine Tadros, Al Jazeera's correspondent in Gaza, said supplies of European Union-funded fuel destined for Gaza's only power plant would only last a few days - raising fears that hospitals and other key insitutions will continue to be hit by power cuts and blackouts.
Temporary respite
"This is, perhaps, a bit of respite for Palestinians but there is no security in the coming week ahead that they will have enough power to keep businesses going," she said.
"The cycle is continuing whereby Israel drips in supplies but a few days later [Gazans] are back at the same point where they are running out of supplies... there's no security because they have no idea of when the crossing will be open again."
Israel's decision to temporarily open the crossings comes just one day after doctors at Gaza's biggest hospital said they had been forced to rely on a faulty generator to operate life-saving equipment.
Hassan Khalaf, director of Shifa hospital, said lives were being put a risk and that the intensive care unit could be rendered useless.
Israel closed all of its crossings with Gaza on November 5 in response to rocket attacks launched by Palestinian fighters within the Strip.
The Israelis have repeatedly said that they will not lift the blockade on Gaza until the rocket attacks end.
A Palestinian official said the Israelis agreed to temporarily lift the blockade after Egyptian mediators intervened, asking Israel to let in essential humanitarian supplies while calling on Palestinian fighters to simultaneously stop rocket fire.
Both sides blame each other for breaching a fragile five-month old ceasefire, also brokered by the Egyptians.
However, both say they want the truce, that is due to expire in December, to hold.