Palestinian Authority President Mahmoud Abbas on Wednesday underscored the complexity of resolving the Gaza Strip crisis when he insisted anew that his administration alone should be responsible for the coastal enclave's border crossings.

Speaking to reporters after meeting here with Egyptian President Hosni Mubarak, Abbas said he would not negotiate with Hamas, the militant party that controls the Gaza Strip, to end a security breach that has allowed more than 500,000 Palestinians to cross into Egypt through the Rafah post in the last week.

"There is only one authority," said Abbas, referring to his government. "Hamas is not a legitimate party, but an overthrowing party."

Abbas' remarks are not surprising, but they come as Egypt, which has endured the brunt of the border breakdown, attempts to mediate between Hamas and the Palestinian Authority. Top Hamas officials, including Khaled Meshaal, who is based in Syria, and Mahmoud Zahar, began arriving in Cairo for separate meetings with Omar Suleiman, director of the Egyptian intelligence service.

Mubarak is opposed to Hamas' control over the Gaza Strip and fears that the Islamist group's militant fervor could spread to Egypt. Cairo's favor rests with the Palestinian Authority, as indicated by Mubarak's decision to meet with Abbas but not Hamas leaders.

The United States, Israel and Egypt support returning to a 2005 agreement that gave supervision of the border to the Palestinian Authority and a team of European monitors. That approach collapsed last year when Hamas fighters routed Fatah forces loyal to Abbas and seized the Gaza Strip. The clashes came as attempts at a unity government between Fatah and Hamas, which won parliamentary elections in January 2006, foundered.

The chaos intensified last week when masked gunmen blew open the border wall after Israel cut fuel supplies to Gaza in retaliation for rocket barrages. On Wednesday, Israel's Supreme Court upheld the fuel restrictions, rejecting arguments by Israeli human rights groups that they deprived Gaza's 1.5 million people of basic humanitarian needs.

Citing the 2005 border agreement, Abbas told reporters Wednesday: "We must commit ourselves to the conventions that have been reached with the Israeli side and under the American and European Union urgings."

European officials have said they would reinstate monitors at the Rafah crossing if Hamas guards were not present.

Hamas spokesman Fawzi Barhoum told the RNA news agency that Hamas would not return to the 2005 agreement. Hamas' Zahar told reporters that, at least in the short-term, Egypt should "keep the border crossing open as it is our only opening to the world."

Abbas said he would not meet with Hamas "unless they comply with the conditions we have put forward to back off their coup, recognize international legitimacy and accept new early elections."

Crowds at the border crossing have thinned. Egyptian and Hamas guards are cooperating and limiting pedestrian and vehicle flow through one passage. Rain and closed stores in Egypt also have greatly reduced the surge.