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WASHINGTON – Diplomats searching for a way to end the fighting in the Gaza Strip have been working on two possible solutions: a bare-bones deal that offers Israel and Hamas little but a halt to fighting and a more ambitious agreement that would try to meet some of each side’s longer-term goals. Neither approach seems to be working.

The “less for less” plan, the core of a proposal floated by Egypt in the first days of the conflict, worked in past conflicts, including the 2012 battle between Israel and Hamas, the Palestinian militant group that controls Gaza, because it gave each side a way to disengage without rewarding the other.

This time, however, both sides want to keep fighting. Israel believes it needs to eliminate Hamas’ tunnels and rocket arsenal, and Hamas thinks it can win political concessions from the Israelis as casualties mount.

Indeed, the fighting Tuesday reached a new level of destruction and bloodletting as Israeli forces unleashed some of the most intense bombardments of the 3-week-old war, flattening the home of Hamas’ top political leader in the Gaza Strip, damaging the offices of an affiliated television station and knocking out the densely populated coastal enclave’s only power station, according to Palestinian officials.

The strikes killed more than 100 Palestinians, raising the death toll in the campaign to more than 1,200, including at least 53 soldiers and three civilians on the Israeli side. The latest Israeli casualties included five soldiers killed when a group of heavily armed militants emerged from a tunnel near a kibbutz called Nahal Oz and fired at them with anti-tank missiles, the military said.

Each side has made clear it wouldn’t be satisfied with a return to the status quo, which for Israel would mean continued vulnerability to Hamas rocket fire and for Hamas would mean a continuation of the blockade on most commerce with Gaza. A status quo agreement would set up conditions for a new war in a couple of years, both sides seem to believe.

The “more for more” idea, as seen in the plan offered in recent days by Secretary of State John F. Kerry, has also been a tough sell. It would involve some measure of disarmament by Hamas in exchange for a freeing of some restrictions on Gaza and probably a large, international aid package.

That sort of deal would meet goals each side desires, but neither side has been willing to see the other rewarded.

“Israel doesn’t want to give Hamas anything that would make it stronger, or give it a political gain. And that’s exactly what Hamas is looking for,” said Robert Danin, a longtime U.S. diplomat in the Middle East, who is now with the Council on Foreign Relations. “So they’re locked in a zero-sum game.”

The prospects for a deal have looked especially bleak as this week began.

Israeli Prime Minister Benjamin Netanyahu, in a television appearance Monday, said the military offensive may take “a long time.”

Kerry returned to Washington over the weekend with just a few hours’ halt in fighting to show for six days of shuttle diplomacy in the Middle East and Europe.

Although the spiraling death toll has increased international pressure for a deal, the diplomatic mechanism has appeared damaged. Particularly troubling for future peacemaking efforts has been a degree of open conflict between the United States and Israel not seen in many years during a crisis of this sort.

Israeli officials quoted anonymously in the Israeli news media attacked Kerry in surprisingly personal terms over the weekend. Channel 2 quoted unidentified Cabinet ministers on Saturday saying he was “negligent” and “incapable of handling the most basic matters.”

They contended that Kerry’s cease-fire proposal was slanted toward the Palestinians and didn’t consider Israel’s need to continue destroying the two dozen or so tunnels built by Hamas into Israeli territory.

Kerry and other U.S. officials pushed back strongly, condemning Israelis for leaking the proposal and insisting that what the Israelis were describing as a final offer was only an initial draft.

The criticism was “not the way allies and partners treat each other,” State Department spokeswoman Jen Psaki said.

The criticism of Kerry has come from all parts of the Israeli political spectrum and reflects in part deep feelings about what Israelis see as a grave military threat, said Michele Dunne, a Mideast specialist at Carnegie Endowment for International Peace.

It may also reflect a sense among some officials in Israel that “if you push back against this administration, it works,” she said. She noted that the administration abandoned its call for a freeze on Israeli settlements in the West Bank in 2009 after strong push-back from Israeli leaders and their American supporters.

Those frictions aren’t the only obstacles in the path of a diplomatic solution.

In past Mideast crises, one or more world powers have usually had significant leverage over key players, which has helped to bring about an agreement. If not the United States, then Egypt or Saudi Arabia could step into the mediator role.

This year, however, the United States is seen in the region as a country seeking to reduce its international role. The military government in Egypt is anti-Islamist and lacks the special influence over Hamas that its predecessors had. It also wants to limit its involvement in Gaza, which it views as a costly burden.