Both sides have blamed each other of breaking the five-month ceasefire that led to Israel's imposition of the blockade, which is causing a humanitarian crisis in Gaza.
The borders with Israel had been opened on Monday and about 45 lorries were allowed through the Kerem Shalom crossing, including 10 UN vehicles carrying food and medical supplies.
Another 15 truckloads of supplies were let through the Karni crossing with an unspecified number also passing via the Nahal Ouz opening.
Humanitarian agencies have said that the supplies are reaching the Gaza Strip are not enough to sustain the population.
A lack of fuel for Gaza's power plants and limited medical supplies have put hospitals at serious risk of being rendered useless.
The UN has said that the blockade is a "direct contravention of international human rights and humanitarian law" and should be ended immediately.
Israel closed all of its crossings with Gaza on November 5 following rocket attacks launched by Palestinian fighters within the Strip and has refused to lift the blockade until the 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.
Several Israelis have been injured by Palestinian rocket fire in the past couple of weeks.