"The border will go back as normal," said Hossam Zaki, an Egyptian foreign ministry spokesman.
"The current situation is only an exception and for temporary reasons."
The issue has turned into a political row between Egypt and Israel.
Matan Vilnai, the Israeli deputy defence minister, said Israel gradually wants to relinquish responsibility for Gaza, now that the territory's border with Egypt has been blown open.
Egypt has angrily rejected the suggestion and said it would not change border arrangements.
The blasts that made holes in Gaza's border with Egypt came after the Israeli government blocked fuel and aid shipments into Gaza beginning last week.
A series of Israeli air raids on Gaza over the past 10 days also claimed the lives of more than 40 people, most of them fighters.
Israel says its actions are aimed at halting rockets fired into southern Israel from Gaza by Hamas fighters and denies that it is engaging in "collective punishment" against the Palestinian people.
But Salam Fayyad, the Palestinian prime minister whose government is based in the West Bank and has no control over Gaza, called the situation in the Gaza Strip "absolutely disastrous".
"This is a pressure cooker kind of situation and a very damaging situation - one that threatens to spiral out of control," Fayyad told delegates at the World Economic Forum at Davos in Switzerland.
'Peace efforts threatened'
Early on Friday, an Israeli air strike on a car in the town of Rafah killed at least two Palestinian fighters, security officials and medical staff said.
An Israeli army spokeswoman confirmed the military had carried out an air strike, saying that the target had been "terror operatives".
Jordan's King Abdullah II told George Bush, the US president, on Thursday that Israel's blockade of the Gaza Strip threatened peace efforts in the Middle East.
Bush has said he believes a peace agreement between Palestinians and Israelis is possible by the time he leaves office in early 2009.
"Israel must refrain from unilateral actions, including the imposition of economic siege and escalation of military operations against the Palestinian people," an official statement quoted Abdullah as saying in a telephone conversation with Bush.
"These policies threaten to undermine efforts made over the past weeks and months to advance the peace process."
Boost for Hamas
The border breach has given a popularity boost to Hamas, which took control of the Gaza Strip in June last year, allowing the group to claim it broke the Israeli siege.
"Hamas has won the strategic battle," said Abu Ali, a 45-year-old Gazan businessman who was on the Egyptian side to buy materials for his construction company.
"Ask anyone here how they reached this place, and they will tell you it was because of Hamas."
Also on Thursday, Unrwa, the UN agency aiding Palestinian refugees, urged Arab Gulf countries to provide about $9.8m in aid money to Gaza.
"The [Israeli] siege has led to a significant increase in the burden on Palestinian civilians," said Peter Ford, an Unrwa representative.
He said the money would buy food, medicine and other supplies for Gaza's residents.