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Under pressure from the Palestinian public, the political factions that have ruled a divided Palestine for the last five years are making what each calls a sincere effort to reconcile. Mahmoud Abbas, who heads the Fatah party that governs the West Bank, has accepted an invitation from rival Hamas to travel to the Gaza Strip. The visit would be the first since Hamas drove Fatah operatives out of Gaza in 2007 — throwing some off from the tops of buildings — in the turmoil that followed Hamas' surprise victory in elections months earlier.

It's too early to gauge the sincerity of the overtures, but both factions feel intense pressure to bury the hatchet and put an end to what ordinary Palestinians call an intolerable distraction from the greater issue of ending Israel's occupation of both the West Bank and Gaza since the Six Day War in 1967. Tuesday saw pro-unity demonstrations in several Palestinian cities, and though the young organizers complained the events were marred by both factions' efforts to co-opt the events — Hamas sent in both its both its own marchers and riot police — the effort bore immediate fruit. Ismail Haniyeh, the top Hamas official in Gaza, went on television to invite Abbas to the coastal enclave. Abbas accepted, and began preparations to travel, perhaps next week.

"We have to break this vicious cycle," says Jabril Rajoub, a member of Fatah's central committee. "In Fatah there is almost a consensus that the right way to assure national aspirations should come through unity."

Hamas appears more divided, the split running between leaders in Gaza and in Syria, where the party maintains its headquarters. Analysts say the leadership in Gaza, as opposed to that in Damascus, is more inclined toward reconciling with Fatah, given the intensity of public pressure. At least 10,000 people demonstrated for unity last week, and youth organizers have persevered despite arrests and beatings of leaders and even journalists covering the protests.

Others, including the leadership in Damascus, are reluctant to begin a process that may end with Hamas surrendering control of Gaza — and at least the appearance of abandoning the group's core principles of armed resistance against a Jewish state it says has no right to exist. The 51 mortars launched into Israel over the weekend — the first shells Hamas has accepted responsibility for in two years — did not come out of the blue. The barrage was widely understood as an expression of defiance by Hamas' military wing. In provoking a nearly automatic reprisal from the Israeli military, the massive launch also helps shift the conversation from peace to war.

It's a conversation many Palestinians have grown weary of. Rajoub, who led Fatah security operations on the West Bank under Yasser Arafat, is among the former militants who now say nonviolence is the logical way forward. In a lengthy interview with TIME, he sketched a strategy that largely dovetails with the aims of the March 15 Movement, the leaderless youth campaign that aims to channel the populist spirit of Egypt and Tunisia into a new paradigm for the conflict with Israel. Their plan only begins with reconciliation between Fatah and Hamas. It then calls for large scale, resolutely nonviolent marches on Israeli checkpoints and the separation barrier, marshalling international public opinion to push Israel to negotiate terms of its withdrawal, paving the way to statehood.

"I myself believe in that," Rajoub says. "And I think promoting such a type of resistance is part of my faction's next strategy. It's not a secret that the nonviolent struggle is a preferable means in the next few months.... The Israelis want to keep this image of the Palestinian people [associated with] terror attacks, suicide bombs and so on, instead of the humanitarian approach."

Fatah aims to beckon Hamas to the high road with it. As Rajoub lays it out, the factions would unite on terms that maximize "international legitimacy" for Palestinian statehood by embracing nonviolence. The Islamist group would be obliged to adopt the policy of "one gun, one law" — that is, a single civil authority with control over security — and disarm militias in Gaza just as Fatah did on the West Bank. Such a move might reassure Israel, which refuses to negotiate with Hamas as long as its charter calls for the elimination of the Jewish State. It would also demonstrate to the international community that Palestine has achieved the most fundamental requirement of statehood: a state monopoly on violence.

That vision isn't winning easy converts, though. "This is all B.S.," says Mahmoud Musleh, a Hamas member in Ramallah, where he was elected to the Palestinian parliament that ceased operating when Gaza and the West Bank split. "If unity is going to happen, it's not going to happen in the media. It's going to happen in private."

Israel is an even tougher sell. "Hamas continues to call for our liquidation," prime minister Benjamin Netanyahu said on CNN last week. "So what am I going to negotiate with them? The method of our decapitation? The method of their exterminating us?"

The Fatah strategy, however, is to reach past the Jewish State to win the backing of the international community. In September, the Palestinian Authority that Abbas heads on the West Bank is planning to conclude a two-year "nation building" effort with a declaration of statehood. In the meantime, Fatah plans to continue asking individual governments to recognize a Palestinian state based on the 1967 borders of Gaza and the West Bank, a process that could lead to a vote in the United Nations General Assembly.

Outstanding questions remain about elections, which Abbas wants to call within months. But Rajoub, whose brother is a senior Hamas official, says "the people of Hamas, most of them," are open to reconciliation. Even Musleh, the Hamas lawmaker who discounts the current overtures as windowdressing, sees possibilities in the revolutions sweeping the Arab world. Could Hamas put down its guns and march? "Yes, if everyone agrees on the same thing, yes, why not?" Musleh says. "Yemenis are well-armed, but they don't want to shoot. They left their weapons at home and went out. This is possible, maybe."

• Karl Vick / Ramallah
• A reconciliation seems to be in the works but conflicting interests and policies may yet prevent the West Bank and Gaza from being a single political unit