Such a deal remains elusive, in part because Hamas refuses to disarm - a key Israeli condition for lifting the blockade. Hamas also remains locked in bitter disputes with its main rival, the Fatah movement led by Western-backed President Mahmoud Abbas, whom the international community views as a central guarantor of any new arrangement for Gaza.
Three weeks after the end of the latest Israel-Hamas war, the third in five years, it is still unclear when Egyptian-mediated talks between Israel, Hamas and Abbas on Gaza's future will be held.
In the meantime, Israel says it has agreed to allow larger amounts of construction material into Gaza under United Nations supervision to begin reconstruction, though details are sketchy. Israel says tight supervision is needed to prevent Hamas from diverting cement and steel for military use.
The deputy leader of Hamas, Moussa Abu Marzouk, insisted Thursday that Hamas won the war, despite the apparent military setbacks and massive loss to Gaza.
He said his group's popularity among Palestinians has increased and that it would likely defeat Abbas and his Fatah movement if elections were held today. Early this month, a survey conducted by a prominent West Bank pollster found a significant increase in support for Hamas after the war.
Abu Marzouk warned that failure to negotiate a new Gaza deal and a lifting of the blockade would "lead to another war."
"We don't want that, and the Israelis, I guess, don't like to see that (war) again," he said in halting English, speaking in an office in a Gaza City high-rise overlooking the Mediterranean.
Abu Marzouk, the deputy of exiled Hamas chief Khaled Mashaal, said the people of Gaza lived in a difficult situation before the war as a result of the blockade.
"We can't put the Palestinians after the war in the same situation," said Abu Marzouk, who has lived in Egypt for the past three years but has visited Gaza several times. "They (the Israelis) have to change their policy."
Israel and Egypt sealed Gaza's borders after Hamas seized the territory from Fatah in 2007.
Conditions in Gaza deteriorated further after Egypt sealed hundreds of smuggling tunnels under its border with Gaza a year ago and tightened travel restrictions for Gaza residents. The closure of the tunnels, a major lifeline for Gaza's economy, helped drive up unemployment, with about two-thirds of those under the age of 30 now without jobs.
Hamas and Fatah reached a unity deal before the war, after several failed attempts following the 2007 Hamas takeover. Under that deal, Abbas was to head a unity government of technocrats in the West Bank and Gaza -- terms Hamas accepted in hopes its former rival could extract it from a financial crisis triggered by the new border restrictions.
Major disputes were left unresolved, however, and the unity government never got off the ground.
The international community expects Abbas to play a key role in any new arrangement for Gaza, including deploying his forces at Gaza's border crossings, but he won't be able to do so if he can't reach an agreement with Hamas on the new government.
At issue is how much authority Hamas is willing to cede to Abbas, particularly over the Gaza security forces. Hamas has balked at the idea, and little seemed to have changed since the war.
On Thursday, both sides warned they had other options if the unity deal fell through.
Azzam al-Ahmed, a senior Fatah negotiator, said Hamas must abide by decisions of the unity government, which should assume control over the security forces in Gaza. "Hamas cannot take Gaza to war next time," he said.
In Gaza, senior Hamas official Mahmoud al Zahar said Fatah didn't consult Hamas when it signed interim peace deals with Israel two decades ago. He added that any technocratic government should serve no longer than six months.
"Then we will think about alternatives because we cannot let the Palestinian people be subjected to those who can't deliver any achievements," he said.
During 50 days of fighting, Israel launched thousands of airstrikes at Hamas-linked targets in Gaza, killing more than 2,100 Palestinians, the vast majority civilians, and destroying more than 18,000 homes, according to UN officials.
Gaza-based terror groups, in turn, launched thousands of rockets and mortar shells at Israeli citizens, many of which were intercepted by the Iron Dome anti-missile system. Nonetheless, 66 soldiers and six civilians were killed.
Israel said it destroyed Hamas' network of attack tunnels under the Gaza-Israel border and that the group's arsenal of about 10,000 rockets was reduced by two-thirds.