The hunt for a way to end fighting in the Gaza Strip that has killed more than 800 people is hobbled by a head-spinning litany of complications, chief among them for the United States that one combatant — Israel — is a close ally and the other — Hamas — a blacklisted semi-enemy.

It’s hard to be a broker when you can’t even talk to one side, as Secretary of State John F. Kerry experienced during five days of peacemaking efforts this week.

Kerry had hoped to announce a temporary truce on Friday, envisaging a cease-fire that would begin over the weekend and last perhaps a week, allowing time for larger negotiations that might make another fight in Gaza less likely.

Israel and Hamas instead agreed to a 12-hour “humanitarian pause” on Saturday, and the fighting looked sure to resume afterward.

Late Friday, Israeli media reported that Israel’s security cabinet had unanimously rejected the larger cease-fire proposal in its current form. Kerry acknowledged that the effort had fallen short but said he and other diplomats would continue working to halt the violence.

“Gaps have been significantly narrowed,” he said, according to the Associated Press. “It can be achieved, if we work through some of the issues that are important for the parties.”

The Obama administration is squeezed between loyalty to Israel and the rising international criticism of Israel over what is frequently seen as callous inattention to civilian casualties and overwhelming use of force.

Israel responds that it protects civilians while Hamas uses them as human shields, but that does not make the Americans’ peacemaking task any easier.

Kerry’s push for a truce included one day of traditional shuttle diplomacy, making a circuit from Egypt to Israel to the West Bank and back again. Much of the rest of the time he was on the phone.

On Kerry’s speed dial: the foreign ministers of Turkey and Qatar, Muslim diplomats with their own agendas but an open line to Hamas leaders. Hamas leader Khaled Meshal is based in Qatar’s capital, Doha.

Kerry also met twice with the intelligence chief for the Palestinian Authority, who ran interference during the lengthy split between the Palestinian Fatah faction, which talks to Israel and the United States, and Hamas, which talks to neither.

The Palestinian split is its own complication in resolving the
18-day conflict in Gaza, which has been controlled exclusively by Hamas since 2007. The militant group has long pledged to eradicate Israel, and the United States and Israel consider it a terrorist group. U.S. officials are barred from direct dealings with Hamas.

Militants affiliated with Hamas, or protected by it, use Gaza as a launching pad for rockets that terrorize Israel despite being mostly ineffectual and dig tunnels on the Israeli border that Israel claims are used for attempted terrorist raids.

Hamas and Fatah formally reconciled this spring, which along with renewed Israeli settlement building, scuppered Kerry’s larger effort to resolve the decades-old Israeli-Palestinian conflict. Unification did nothing to stop Hamas rockets fired into Israel before the current active warfare, and Israel says more than 2,000 rockets have been launched from Gaza since fighting began July 8.

Palestinian Authority President Mahmoud Abbas ran his own circuit diplomacy this week but has been unable to win concessions for Hamas from Israel or to persuade the militants to relent.

There are also the problems of Hamas’s own growing isolation and weakness, which leave the militants with less to lose by continuing their fight against Israel, and the diminished influence of Egypt, an American partner, as a go-between.

Those factors make a deal much harder to reach now than when Hamas and Israel last traded fire in 2012. Then, an eight-day conflict ended with a cease-fire brokered largely by Egyptian President Mohamed Morsi and Secretary of State Hillary Rodham Clinton.

Morsi was a Muslim Brotherhood-backed leader with clear pull among the militants, and his intercession for a cease-fire gave him new gravitas as a statesman.

The halo effect proved short-lived, but the cease-fire held even as Morsi was ousted in a military coup last summer and replaced by a military-backed Egyptian government that is deeply suspicious of the Hamas militants next door.

Egyptian President Abdel Fatah al-Sissi has banned the Muslim Brotherhood and snapped shut the key Rafah border crossing between Egypt and Gaza.

The new Egyptian government looks and feels much like the old, pre-Arab Spring military dictatorship of Hosni Mubarak. But where Mubarak was a trusted Middle East power broker and bulwark for American aims, the Obama administration has not yet decided how much to rely on Sissi or how cozy to appear with Egypt.

That leaves Kerry in the uncomfortable position of owing gratitude to Egypt for keeping a lid on Islamist unrest and for quiet cooperation with Israel but being unable to ask for Egyptian help as an intermediary with the militants.

An Egyptian cease-fire proposal proffered last week was accepted by Israel but rejected by Hamas as insufficient. Kerry has sought to amend the offer without offending the Egyptian authors.

Then there is the double-sided question of whether Israel is ready to halt its military campaign and whether Hamas sees it in its interest to agree.

Israel’s air and ground campaign has gone on far longer, and pushed far deeper into Gaza, than seemed likely at the start. Israel ignored U.S. admonitions against a ground invasion and has put off rising international criticism of the civilian death toll.

It was not clear Friday what happens next, now that Israel’s cabinet has rejected the U.S.-
backed cease-fire proposal.

Meanwhile, Hamas is having a moment. The group’s star has fallen far since 2012, as Egypt withdrew support, former Syrian patrons turned inward in civil war and Iran cooled to its former client. But the current conflict is drawing international attention to the main Hamas aim of ending the Israeli siege of Gaza.

While sympathy for Hamas is thin everywhere, the mounting deaths and episodes such as the shelling of a U.N. school in Gaza on Thursday may fuel outrage toward Israel and improve the militants’ bargaining position.