JERUSALEM — Egypt said Monday that it preferred that the Palestinian Authority president, Mahmoud Abbas, take control of the breached border between Gaza and Egypt, seeming to exclude Hamas, the Islamist group that took control of Gaza from Abbas in June.

The Egyptian foreign minister, Ahmed Aboul Gheit, told the United States and the European Union that Israel should cooperate with efforts to control border crossings "through the deployment of the Palestinian Authority" and "European Union monitors," the ministry said in a statement. Aboul Gheit emphasized that Egypt would "carry out a gradual control of the Egyptian border with the Gaza Strip and bring the situation back to an acceptable condition," the statement said.

Hamas blew up the Israeli-built wall between Gaza and the Egyptian border early Wednesday after Israel had sealed off Gaza to try to stop rocket and mortar fire into Israel. Since then, hundreds of thousands of Palestinians have traveled into and out of the northern Sinai, buying food, medicine, consumer goods and livestock.

Egypt has slowly tried to resecure the border, refusing to allow the resupply of goods to the border towns of El Arish and Egyptian Rafah.

Shops in El Arish and Rafah have largely run out of goods to sell, and tempers between Palestinians and Egyptians have begun to fray.

Egypt appears to want to return the Rafah crossing to its situation before June, when European Union officials monitored the border and Israel kept watch by video link. But even then security problems often kept the Rafah crossing shut.

Hamas, which considers itself the legitimate Palestinian government because of its electoral victory in January 2006, has made it clear that it wants a role in operating the crossing. Israel also regards the old arrangement as problematic, given Hamas' control over Gaza, and wants Egypt to do more to stop the movement of militants and weapons.

Since Hamas routed Fatah forces loyal to Abbas in early June, the Rafah crossing had been shut, but Egypt now seems unwilling to shut it completely again. At other crossings, Israel has allowed in only bare necessities, and it has been cutting fuel supplies to ensure that Gazan life is uncomfortable at best so long as militants are firing rockets into Israel.

But Israel's effort to seal off Gaza backfired with the border breach, and on Sunday the government agreed to resume sharply limited supplies of gasoline and diesel to Gaza, as well as industrial diesel for the Gaza power plant.