The gaps remain wide, especially between Israel and Hamas.
Israel says it has inflicted a painful blow to Hamas' military capabilities in the monthlong fighting and wants to make sure the group cannot re-arm if border restrictions are eased.
"The extent to which we are going to be ready to cooperate with the efforts to have better access and movement in Gaza will deeply depend on the kind of arrangements that would secure our peace and security," said Yossi Kuperwasser, a senior official in Israel's Strategic Affairs Ministry.
Hamas, in turn, has signaled flexibility on ceding some authority to Abbas in Gaza, but insists on having a say on reconstruction and that it will not disarm.
Izzat Rishq, a senior Hamas official, said disarming isn't up for discussion.
"We'd take the life of anyone who tries to take the weapons of resistance," he told The Associated Press.
Despite such tough talk, Hamas is in a position of relative weakness.
The Islamic militant group's fortunes changed dramatically last year after the Egyptian military deposed a Hamas-friendly government in Cairo and began closing hundreds of smuggling tunnels under the Gaza-Egypt border.
The closures deprived Hamas of a key source of revenue the taxation of goods brought through the tunnels and prevented weapons and cash destined for Hamas from flowing into Gaza.
By this spring, Hamas was in such a severe financial crisis that it accepted a reconciliation deal with Abbas. Under that agreement, an Abbas-led government was to run both the West Bank and Gaza, though thorny issues were put off, including Hamas' insistence that it retain control over its security forces. The unity government was stumbling by the time Israel-Hamas fighting erupted on July 8.
Even before the war, Gaza was in bad shape because of the prolonged blockade.
Unemployment in the impoverished territory of 1.8 million people had risen well above 50 percent, in part because of Egypt's tunnel closures. Only half of Gaza's electricity needs were being met, and the closure prevented most Gaza residents from travel.
After four weeks of intensive fighting, including close to 5,000 Israeli strikes on Gaza targets, the devastation is widespread.
According to initial figures from Gaza's main U.N. aid agency, some 10,000 homes were destroyed or damaged beyond repair. Gaza's only power plant was forced to shut down last week after being shelled by Israel, and repairs will take months, Gaza officials said.
One of the hardest-hit areas was the southern town of Rafah, where intense shelling over the weekend appeared to have spared little. Mosques, homes, offices, stores and at least one school either lay in ruins or were badly damaged, hit by shrapnel or gunfire.
After Tuesday's cease-fire took effect at 8 a.m. (0500 GMT), thousands of Rafah residents returned home to try to salvage belongings.
Ahmed Barbakh, a 36-yer-old government employee, emerged from his badly damaged home with a plastic bag containing the birth certificates of his five children and other crucial documents.
A lone chicken was all that was left of the dozens he raised at home. "I am not taking it. What am I supposed to do with a chicken now? I need a place to live with my wife and children," Barbakh said as he made his way out of his crushed home.
Nearly 1,900 Palestinians have been killed, the vast majority civilians, according to Gaza health officials and U.N. figures. On the Israeli side, 64 soldiers and three civilians were killed.
The truce is to remain in effect for at least three days, with an expectation that it will be extended to allow Cairo talks on a Gaza solution to proceed. Both the United States and the U.N. are sending representatives.
Mohammed Mustafa, a deputy prime minister in the Abbas-led government, said he has already started preparing a Gaza reconstruction plan that would be presented at an international pledging conference in Norway.
He said the usual lineup of donors the United States, European Union, Japan, Arab states and international organizations like the World Bank are likely to be there.
Norwegian Foreign Ministry spokeswoman Veslemoey Salvesen confirmed that Norway will host the conference in early September in Oslo, but said no date has been set.
International Mideast envoy Tony Blair is also involved in arranging the conference, his office said.
Mustafa, an economist, said in a phone interview from the West Bank that the war caused at least $6 billion in immediate damage, but the figure is expected to rise once inspectors can survey the territory.
Abbas expects to take the lead in any reconstruction effort, Mustafa said, suggesting that Hamas should step aside and enable the Abbas-led unity government to carry out the task. "This is the deal, this is my understanding of our role in the future," he said.
Rishq, the Hamas official, said his movement does not have a problem with Abbas raising money for Gaza, but expects to have a say about rebuilding the territory. "I think the appropriate approach for rebuilding Gaza is having a national commission," he said.
In the Cairo talks, Hamas is part of a Palestinian delegation led by an Abbas confidant, Azzam al-Ahmed, and also includes members of other Palestinian factions.
The Palestinian delegation has presented a list of demands, including a lifting of the border closure and a release of Palestinian prisoners arrested by Israel in a recent West Bank sweep.
A three-member Israeli delegation arrived in Cairo late Tuesday, according to an Egyptian airport official who spoke on condition of anonymity because he was not authorized to speak to the media. Israeli government officials have refused to discuss the delegation's travel plans or its composition.
In Washington, State Department spokeswoman Jen Psaki said the U.S. expects to participate in the Cairo talks to negotiate a longer-term truce between Israel and Hamas. It's still unclear what role the U.S. would take, or when that would happen, she said, but "our effort and our engagement on this process from the beginning has been welcomed by the parties."
The United Nations will be represented in Cairo by Robert Serry, the U.N. special coordinator for the Middle East peace process, a spokeswoman said.
Kuperwasser, the Israeli official, told reporters earlier Tuesday that having forces loyal to Abbas deployed at the Gaza crossings would likely not be enough to allow restrictions to be eased, and that there should also be international supervision.
"Yes, they (Abbas' forces) can have a role in the crossings, but we can't say we can fully trust just Abu Mazen," he said, referring to Abbas. "It's got to be something more robust. International and Egyptian elements should be involved in it. And other means of supervision should be involved as well."
One key sticking point will be the import of construction materials, including cement and steel. Such materials will be needed in huge quantities for rebuilding Gaza, but Israel has said they were diverted in the past by Hamas for military use, such as building attack tunnels under the Gaza-Israel border.
During the last month of fighting, Israel said it destroyed 32 such tunnels.
Michael reported from Cairo. Associated Press writers Mohammed Daraghmeh in Ramallah, Yousur Alhlou in Jerusalem, Lara Jakes in Washington and Edith M. Lederer at the United Nations contributed to this report.