As it wrestles with this predicament, Hamas is trying to turn up the pressure on Israel - most notably by encouraging weekly mass protests along the Gaza border fence - without provoking an all-out military response that analysts say the group might be too weak to withstand.
The immediate aim, analysts say, is to loosen the years-old blockade imposed on Gaza by Israel, Egypt and the rival Palestinian Authority, which controls the Occupied West Bank.
Some Hamas leaders have also seen the protests as a chance for Gazans to vent and direct their anger at Israel.
But as the Palestinian death toll in the protests has mounted with each passing week, so has public dismay with the militant group.
Hamas, which the United States considers a terrorist organisation, is also trying to strike an awkward balance between its traditional strategy of armed resistance against Israel and the imperative to preserve enough calm in Gaza so the group can govern it.
On Tuesday, another militant Palestinian group, Islamic Jihad, fired scores of mortar shell and rockets from Gaza into southern Israel, a dramatic escalation that analysts say could not have happened without Hamas’s knowledge and perhaps support.
Israel hit Gaza with a blitz of air strikes, the biggest seen since the devastating 2014 Israeli assault on Gaza.
Hamas’s armed wing asserted joint responsibility for the shelling, and its compounds were struck by Israeli jets overnight.
But the group’s political leadership swiftly announced a ceasefire after talks with Egyptian mediators - widely seen as a sign that Hamas has no interest in going to war.
At the same time, the group’s leadership is considering concessions to Israel and the Palestinian Authority, according to the Israeli media, Arab press reports and analysts.
The aim would be to win an easing of restrictions on Gaza that could improve conditions for its 2 million inhabitants.
Unemployment in the territory is running at more than 40 per cent, and the infrastructure is collapsing, with residents getting only four hours of electricity a day and hospitals reporting shortages of medicine and other crucial supplies.
According to the United Nations, the territory will be “unlivable” by 2020.
“Hamas is really under pressure. They have very limited options. They are ready to commit to any security arrangements,” said Ebrahim Al Madhoun, a columnist at the Hamas-affiliated journal Al Risala. To alleviate suffering in Gaza and retain power, he said, Hamas would be willing even to halt attacks on Israel.
Al Madhoun said the current protests are a “last resort” for Hamas.
“They didn’t have a choice,” he said.
“It was the only way for them to try to get out of this deep crisis in Gaza.”
Violent confrontation would only deepen Gaza’s misery, and Hamas, which could have trouble replenishing its weapons stocks, might not survive another war with Israel, analysts say.
Hamas’s leader in Gaza, Yehiya Sinwar, said the group “will continue in the path of popular resistance and will do everything possible to prevent the demonstrations from spilling into armed conflict.”
Speaking in a May interview with Al Jazeera news channel however, he suggested that Hamas would escalate its actions if more Palestinians were killed. “It will demand a response from us,” Sinwar said.
The protests on the border fence started as a grass-roots initiative among students and local activists unaffiliated with Hamas.
But the group soon signed on, providing transportation and other logistical support, and Hamas members were among the protesters.
Since late March, mostly unarmed protesters have thronged to the border fence every Friday.
More than 100 Palestinians have been fatally shot by Israeli occupation soldiers, Gaza health officials report.
Some Gazans have complained bitterly that the Hamas-backed protests have produced so many deaths and that living conditions ultimately have not improved.
“The situation is already hard enough, and the demonstrations made it harder,” said Fares Al Alami, 30, a shop owner in Gaza City’s market district.
“It wasn’t the right time for such protests. But I don’t think this government [in Gaza] has any solutions for us.”
The decline of Hamas’s power has marked a stunning turn of fortunes for a movement once seen as an irresistible force in Gaza, where it fought three wars with Israel and has ruled for more than a decade.
Hamas won an upset victory over the dominant Fatah party in legislative elections in Gaza in 2006.
The two sides sparred over forming a unity government and eventually fought street battles in Gaza in 2007, with Hamas emerging as the victor.
The militants went on to preside over a lucrative smuggling economy and were bolstered by the rise of like-minded Islamists in places including Egypt after the Arab Spring uprisings.
But as chaos in the region swirled around it, Hamas lost key allies, notably Egypt’s Muslim Brotherhood, which was ousted from power five years ago in a coup by the country’s current president, Abdul Fattah Al Sissi.
Support from Iran and Syria also waned.
Foreign funding for Hamas dried up. And Al Sissi’s government in Egypt, openly hostile to Hamas, closed the tunnels through which cash, goods and weapons had reached Gaza, depriving the group of a critical source of revenue and stunting its ability to bypass the blockade.
Hamas became so desperate that last year it sought to mend ties with the Palestinian Authority, giving its rival control of Gaza’s border crossings and agreeing to set up a technocratic government.
Those reconciliation efforts, however, have stalled, with each side blaming the other for the impasse.
The Palestinian Authority, trying to force Hamas to turn over control of security forces in Gaza, has imposed its own punitive measures, including withholding funds for the territory’s only power plant and halting the transfer of salaries to authority employees in Gaza.
The Palestinian Authority has also blamed Hamas for the bombing of the motorcade of Palestinian Authority Prime Minister Rami Hamdallah during a visit to Gaza in March.
He survived the explosion. Hamas denied responsibility.
In an apparent effort to lower the temperature after weeks of bloody protests, Al Sissi announced in May that he was opening Egypt’s Rafah crossing with Gaza for the Muslim holy month of Ramadan - the longest opening in four years.
But border authorities in Gaza say passenger traffic remains restricted and the process of coordinating travel is still cumbersome and unclear.
“No concrete vision or initiative to ease the siege has been presented to us” by the international community, Hamas spokesman Hazem Kassem said in an interview.
“We can’t even say that there are talks to lift the blockade.”
According to Kassem, Hamas is in discussions with Egypt, Qatar and the United Nations regarding small steps to ease restrictions on Palestinians in Gaza, including allowing more residents to leave the territory and paying for fuel for the power plant.
“Hamas is stuck. They are stuck because of the economic situation in Gaza and because of problems with Palestinian reconciliation,” said Mukhaimer Abu Sa’ada, a political science professor at Gaza’s Al Azhar University.
But he said Hamas might be able to reach a deal with Israel that would allow more people and goods to enter and exit Gaza in return for the group’s agreeing to halt the manufacture of weapons and stop digging the cross-border tunnels used to ambush Israeli soldiers.
“They realized that military confrontation is very costly to the Palestinians,” he said of Hamas. “For that reason, they are not interested at all in another conflict. But they want an end to the siege. They want a solution.”