Movement across the Gaza-Egypt border slowed to a trickle Tuesday as security forces made progress in sealing off breaches and cold, rainy weather discouraged travelers.

The focus of the weeklong crisis shifted to growing tensions between Egypt and the militant Hamas rulers of Gaza, who are now demanding a role in overseeing the border.

Hundreds of thousands of Palestinians have flooded into Egypt since Hamas militants blasted holes in the border partition so Gazans could escape a tight closure of their territory's borders with Israel and Egypt. Israel had recently sealed its border in response to militant rocket attacks from Gaza.

Over the past few days, Hamas security forces have joined Egyptian border guards supervising traffic at the crossing and helping to repair the breaches. Two large breaches remain open.

Jittery about the chaos, Egypt has invited the rival Palestinian factions, Fatah and Hamas, to talks aimed at ending the crisis.

Palestinian President Mahmoud Abbas of Fatah, who is backed by Arab states, the United States and the European Union, came to Cairo late Tuesday. He said his faction — not Hamas — should control the crossing.

Egypt favors restoring a 2005 international agreement whereby control of the border was shared by Abbas' Palestinian Authority, Israel, and EU monitors. Hamas, which seized control of Gaza last June, had no role in border administration before the Jan. 23 breach.

Abbas has expressed readiness to take on the responsibility of all crossing points in Gaza to solve the crisis, but Hamas is insisting it must have a role and that the old arrangements are no longer valid.

That has created tensions between Hamas and Egypt, and there was little hope for a breakthrough during meetings on Wednesday.

In Gaza, Sami Abu Zuhri, a Hamas spokesman, angrily denounced a return to the previous border arrangements. He said the idea was "an international Israeli conspiracy, in which some regional elements and Ramallah (Abbas' faction) are participating."

Egyptians living near the breached border were growing frustrated with the Palestinian influx, warning that chaos was brewing. Palestinians, facing shortages of food and fuel at home, cleaned out stores in the Egyptian border towns and some residents complained they drove up prices.

Egyptian state-owned newspapers were filled with harsh criticism of Hamas, blaming it for violating Egypt's border and undermining its security. One newspaper, Rose El Youssef, contended that Hamas had used the breach to smuggle weapons and explosive-laden suicide belts into Egypt.

Egyptian officials also are apparently infuriated that the Muslim Brotherhood, the main opposition group in Egypt, is involved in the crisis. It leader Mohammad Mahdi Akef reportedly talked with Hamas' chief in Damascus, Khaled Mashaal, and with Nabil Shaath, a representative of Abbas.

Muslim Brotherhood leaders say they are only trying to help defuse the crisis, although they never try to hide their sympathy for Hamas.

"We believe the crossing is an Egyptian-Palestinian affair. The Europeans and (Israel) should be out of it," Mohammed Sayed Habeeb, the Brotherhood deputy leader, told The Associated Press.

Hamas said it was sending a delegation to Egypt headed by Mashaal and including hard-line Gaza leader Mahmoud Zahar. The Palestinian factions will likely meet separately with Egyptian officials because Abbas has refused to talk to Hamas until the group gives up control of Gaza.