Palestinian analysts say the strength of the Islamists is at a historical high: Hamas is already thought to be more popular in Gaza than Arafat’s larger and more moderate Fatah group. Some of Hamas’s leaders now talk about translating that might into political power. Mahmoud Zahar, one of the group’s leaders in Gaza, asserted last week that Hamas had the infrastructure to take over leadership “politically, financially and socially.” Arafat is worried about Hamas’s ascent and has offered the group membership into the already fractious Palestine Liberation Organization. Mashaal says Hamas will weigh the offer, but he wants Arafat to redraft the PLO’s national covenant, which had called for Israel’s destruction until it was amended in 1998. Others want the PLO to drop its reference to a “secular, democratic” Palestinian state.

Some involved in the conference say Egypt has threatened to impede Hamas’s fund-raising in Arab countries if it doesn’t accept the ceasefire. But Hamas doesn’t seem concerned.