The move has offered some respite from a blockade that had plunged much of the Hamas-ruled territory into darkness and touched off international protests.
But, only 13 truckloads of food and medicine entered Gaza today, short of the 50 Israel had agreed to.
Foreign Ministry spokesman Arye Mekel said the rest would cross in the coming days.
Palestinian Prime Minister Salam Fayad said his administration wanted to assume control of Palestinian border crossings in Gaza.
He said his administration, which is based in the West Bank, was willing to do all it could to ease the situation in Gaza.
