Fighting between militants in Gaza and the Israeli military intensified Tuesday, clouding the prospects of a durable cease-fire as Secretary of State Hillary Rodham Clinton rushed to the region to try to prevent a major escalation of the conflict.

Israeli officials and negotiators from the militant group Hamas, communicating through Egyptian interlocutors, remained at odds late Tuesday over details of the truce that the international community was furiously trying to broker. Among the main sticking points was whether Egypt and the United States could act as guarantors of a peace deal in a region where waves of aggression have come in vicious cycles.

A former senior Israeli official who has been briefed on the negotiations said both sides have made it clear that they prefer a cease-fire to avert a ground invasion by Israel, which could multiply casualties and spark a broader regional conflagration. But neither wants to back down without getting significant concessions, said the former official, who spoke on the condition of anonymity to discuss private negotiations.

The Israelis, the former official said, want a commitment that Egypt will do a better job of policing its porous border with Gaza, which includes dozens of tunnels that are used to smuggle everything from vehicles to long-range rocket parts. Hamas, which rules Gaza, wants Israel to lift its blockade of the enclave, home to 1.7 million Palestinians.

Putting to rest rumors and assertions throughout the day that suggested a cease-fire deal was imminent, Israeli Prime Minister Benjamin Netanyahu made it clear to Clinton that he has not ruled out a ground invasion.

Gaza rocket attacks, Israeli airstrikes double from 2008 conflict

“If there is a possibility of achieving a long-term solution to this problem through diplomatic means, we prefer that,” Netanyahu said. “If not, I’m sure you understand that Israel will have to take whatever action is necessary to defend its people. This is something I don’t have to explain to Americans.”

The impasse was a blow to Egyptian President Mohamed Morsi, who had said earlier Tuesday that he expected a deal within hours. The Israeli military said Gaza militants launched 200 rockets Tuesday, while Israel struck more than 133 targets in Gaza.

Clinton, looking weary after flying across five time zones from Cambodia, where she had been attending a regional summit with President Obama, spoke firmly about her desire to avert greater bloodshed.

“America’s commitment to Israel’s security is rock-solid and unwavering,” Clinton said late Tuesday before sitting down with Netanyahu. “That is why we believe it is essential to de-escalate the situation in Gaza.”

Key sticking points

The former Israeli official briefed on the discussions said a key concern is clearly defining the role that Egypt would play as a guarantor if a deal were reached.

“The cessation of smuggling requires a strong Egyptian role,” the former official said. “I don’t believe Hamas will commit to halt smuggling weapons.”

In her remarks to Netanyahu, Clinton also stressed the pivotal part Egypt stands to play, saying that “as a regional leader and neighbor, Egypt has the opportunity and responsibility to continue playing a crucial and constructive role in this process.”

Israeli negotiators also want the deal to include the establishment of a buffer zone along its border with Gaza to prevent cross-border attacks on Israeli patrols, the former official said.

Hamas has demanded the permanent lifting of the Gaza blockade, the former official said, a concession Israel is unlikely to grant. Israel says the measure is designed to keep militants from smuggling weapons and building bunkers.

Complicating matters, the former official said, the Egyptians are making demands of their own. Cairo wants Hamas to rein in more hard-line militant groups based in Gaza that have formed alliances in recent years with extremists in Egypt’s Sinai Peninsula.

“This is a two-layered deal,” the former official said. “Israel does not want to find itself agreeing to a deal that collapses after two or three weeks.”

A violent day

Tuesday was among the most violent days since Israel’s operation, called Pillar of Defense, began a week ago. The campaign seeks to cripple militant cells in Gaza that have stockpiled enormous caches of rockets that are routinely fired toward southern Israeli towns.

The Israeli military suffered its first casualty of the offensive Tuesday, when an 18-year-old corporal from Emmanuel, an Israeli settlement town in the West Bank, was killed by a rocket in southern Israel. Five other Israeli soldiers were wounded by artillery Tuesday, the military said. A civilian Israeli defense employee was killed in a separate rocket attack in southern Israel, officials said, raising the Israeli death toll to five. More than 130 Palestinians have been killed in Gaza since the fighting began, according to health officials.

The 200 rockets launched by Gaza militants on Tuesday included 14 that landed in populated areas, said Capt. Eytan Buchman, an Israeli military spokesman. Two of those were long-range rockets. One landed in a barren area outside Jerusalem, and the other struck a building in a Tel Aviv suburb.

The rocket attacks “reflect the organization’s intent to target population centers, as well as the increasingly advanced capabilities they have acquired over recent years,” Buchman said.

Israel pounded densely populated Gaza throughout the day from the air and the sea. One of the airstrikes targeted the Islamic National Bank, which Hamas set up to fund operations in Gaza in the face of international sanctions.

The Israeli military distributed leaflets and sent text messages warning Gaza residents to move from certain parts of the border area — a warning that some interpreted as a prelude to a ground invasion.

As the strikes continued, Mohammed Deif, a top Hamas military commander in Gaza, issued a recorded statement exhorting his group’s fighters to keep attacking Israel.

Hamas “must invest all resources to uproot this aggressor from our land,” said Deif, who is in hiding. “The enemy should know that it will pay a heavy price for its heinous crimes against our people.”

In Gaza City, meanwhile, masked Hamas gunmen publicly executed six men suspected to be Israeli spies at a large intersection, the Associated Press reported. Hamas’s military wing accused the men of giving Israel information about fighters and rocket-launching sites. The suspects were forced to lie facedown in the street and shot, and one of the corpses was tied to a motorcycle and dragged through the streets as passersby screamed, “Spy! Spy!”

Visit by U.N. chief

In a surprise visit to Israel on Tuesday, U.N. Secretary General Ban Ki-moon appealed for an end to hostilities, warning that an Israeli ground invasion could spark a destabilizing regional conflict.

“Further escalation would be dangerous and tragic for Palestinians and Israelis and would put the entire region at risk,” he said, speaking alongside Netanyahu. Saying that rocket strikes inside Israel have sown “fear and terror,” Ban added: “Rocket attacks by Palestinian militants targeting Israel must cease immediately.”

Birnbaum reported from Cairo. Karin Brulliard in Jerusalem and Julie Tate in Washington contributed to this report.