Jamal Kaed, the Palestinian commander of southern Gaza said on Tuesday that the border was to be closed by Wednesday evening.
Starting on Tuesday evening, Palestinian security forces will set up roadblocks near the border to prevent cars from reaching the area, he said.
The commander also said Palestinian security forces had confiscated large amounts of marijuana and other illegal drugs along the border.
He noted that the border, once heavily guarded by Israel, had divided many Palestinian families who were able to meet again after Israeli troops withdrew.
More let through
Egyptian troops on Tuesday allowed elated Palestinians to flood across the border with Gaza for a second day, deepening Israeli concerns the crossing will be used to smuggle weapons to Palestinian fighters.
Several hundred Egyptian troops
have taken up border positions
Gazans, long barred by Israeli border guards from entering Egypt, went on a shopping spree in Egyptian towns on Tuesday, hauling home suitcases and boxes full of cheap cigarettes, food, fish and other goods.
Others searched out relatives they had not seen in years.
Israeli forces withdrew from the border early on Monday as they ended their 38-year occupation of the Gaza Strip.
Under a deal with Israel, Egypt has deployed hundreds of troops to guard the border and prevent smuggling into Gaza.
But thousands of Palestinians clambered over the walls along the border on Monday, and Egyptian forces said they were temporarily opening the frontier to allow the Palestinians to blow off steam and reunite with relatives.
Although Egyptian troops attempted to control the crossings in some places on Tuesday, Gazans largely continued to move back and forth freely in the border town of Rafah and other places.
Zalman Shoval, a foreign policy adviser to Israeli Prime Minister Ariel Sharon, said Egypt's failure to stop the border crossings was a cause for concern.
"One would like to hope that what happened there was just a one-time failure by the Egyptian troops to do what is expected of them.
"The great danger is that both people and arms could be smuggled under the unwatchful eyes of the Egyptians - that was the whole purpose of coming to this agreement"
Zalman Shoval, foreign policy adviser to Israel's prime minister
"But if this continues Israel will have to ask the multinational force [in the Sinai] to be a great deal more active in supervising the Egyptian compliance in the commitment it made with Israel," he said.
"The great danger is that both people and arms could be smuggled under the unwatchful eyes of the Egyptians - that was the whole purpose of coming to this agreement," Shoval said.
Egyptian Foreign Minister Ahmed Abou el-Gheit, who headed on Tuesday to New York for the UN General Assembly, issued a statement saying only that Egypt "welcomes the current developments in Gaza with the exit of Israeli troops and settlers".
Egypt has so far deployed several hundred of the 750 troops it is due to station at the border. The full contingent is expected to arrive within about a week.
The streets on the Egyptian side of Rafah, a town that was divided in two by the border, were on Tuesday full of Palestinians, shopping and greeting relatives.