He said the request was made in order to comply with a 2005 agreement between Gaza and Egypt, in which Israel handed over control of the crossing to the PA under the auspices of Mahmoud Abbas, the Palestinian president, in an operation monitored by EU observers.
Hamas rejects any Israeli involvement on the border, which was resealed on Monday, and wants EU observers, who have been waiting in Israel since they were unable to go to work in June, to be based in Egypt.
In June last year, Hamas fought and removed the PA forces from the border.
Abu Gheit said Egypt had proposed "several ideas" for reopening the crossing after it was blown up on January 23 by a group of Palestinians, allowing hundreds of thousands of Palestinians across, but declined to elaborate.
"Egypt rejects the policy of collective punishment and calls on Israel to assume its responsibility," he said.
"Our Palestinian brothers should know that the battle is not with Egypt, but the battle is with Israel."
Abu Gheit called on Hamas leaders inside Gaza to "show wisdom and not to encourage Palestinians to approach the frontier because Egypt cannot accept any provocation."
The closure sparked protests by Palestinians, with a demonstration at the border turning violent late on Monday with stone-throwing, exchanges of gunfire and tear-gas.
Hosni Mubarak, the Egyptian president, in an interview published on Tuesday in a Spanish newspaper, said that Egypt will not allow Palestinians to breach its border with Gaza again.
"It is a mistake to besiege the Palestinians but we will not accept that the border be left open indefinitely. What happened will not be repeated," he told the daily newspaper ABC.
Mubarak rejected any responsibility for Monday's violence at the border in which a Palestinian was shot dead.
"We did not give any order to shoot anyone," he said.
The breach briefly ended seven months of tight closures, imposed by Israel and Egypt in response to the Hamas takeover of the Gaza Strip in June 2007.
Many Gazans used the new passage to rush into Egypt to stock up on basic supplies, including cement, fuel, medicines and foodstuffs.