Diplomatic efforts accelerated on Tuesday to end the lethal confrontation between Israel and Palestinian militants in Gaza on one of the most violent days yet in the conflict, as the United States sent Secretary of State Hillary Rodham Clinton to the Middle East and Egypt’s president and his senior aides expressed confidence that a cease-fire was close.

But by late evening there was no announcement, and Mrs. Clinton said she would be working in coming days to complete an agreement. Appearing beside Prime Minister Benjamin Netanyahu of Israel to speak briefly to the press, Mrs. Clinton said she hoped to achieve an end to the hostilities with a deal that moves “toward a comprehensive peace for all people in the region.”

The diplomatic moves to end the nearly week-old crisis came as the antagonists on both sides intensified their attacks before any cease-fire takes effect.

Israeli aerial and naval forces assaulted several Gaza targets in multiple strikes, including a suspected rocket-launching site near Al Shifa hospital, which killed more than a dozen people. Those deaths brought the total number of fatalities in Gaza so far to more than 130 — roughly half of them civilians, the Gaza Health Ministry said.

A delegation visiting from the Arab League canceled a news conference at the hospital because of the Israeli aerial assaults as wailing ambulances brought victims in, some of them decapitated.

Militants in Gaza fired a barrage of at least 200 rockets into Israel, killing an Israeli soldier — the first military casualty on the Israeli side since the hostilities broke out last week. The Israel Defense Forces said the soldier, identified as Yosef Fartuk, 18, died from a rocket strike that hit an area near Gaza. Israeli officials said a civilian military contractor working near the Gaza border was also killed, bringing the total number of fatalities in Israel from the past week of rocket mayhem to five.

Other Palestinian rockets hit the southern Israeli cities of Beersheba and Ashdod, and longer-range rockets were fired at Tel Aviv and Jerusalem, but neither main city was struck and no casualties were reported. One Gaza rocket hit a building in the Israeli city of Rishon Lezion, just south of Tel Aviv, injuring one person and wrecking the top three floors.

Senior Egyptian officials in Cairo said Israel and Hamas, the militant Islamist group that governs Gaza, were “very close” to a cease-fire agreement that could be announced within hours. “We have not received final approval but I hope to receive it any moment,” said Essam el-Haddad, President Mohamed Morsi’s top foreign affairs adviser.

While holding itself out as an honest broker for truce talks between Israel and Hamas over the Gaza conflict, Egypt’s new government sought on Monday to plunge into the battle over international public opinion on behalf of the Palestinian cause — an arena where the Israelis, more experienced in the world of the free press and democratic politics, have historically dominated.

In Egypt’s most concerted effort to win more global public support for the Palestinians, advisers to Egypt’s President Mohamed Morsi, a former leader of the Muslim Brotherhood who has been an outspoken supporter of Hamas, invited foreign correspondents in Cairo to a background briefing at which a senior Egyptian official sought to blame Israel for the conflict while at the same time maintaining Egypt’s role as an intermediary pressing both sides for peace. “We are against any bloodshed,” the official said repeatedly, arguing that Egypt sought stability and individual freedom for all in the region.

Speaking on condition of anonymity to avoid upsetting the talks with the Israelis, the Egyptian official argued that the West, which supports Israel’s right to defend itself against rocket attacks from Gaza, was essentially blaming the victim.

“It is so strange people are talking about the rights of self-defense,” he said. “The self-defense of whom? Of the occupied people? Of the besieged people? Of the hurt people? No, the self-defense of the most powerful state in the region and the self-defense of the occupying force of Gaza and Palestine. This is what some of the international community are talking about.”

He implicitly compared the leaders of Hamas to George Washington in America or Charles de Gaulle in France: Heros because they resisted foreign occupation by armed force. “Now, there is an occupation going on for decades and these people who are suffering this occupation are trying to resist, are trying to gain their rights,” the official said. “But we are saying no, they don’t have the rights, they have to stay calm, be killed, be occupied, be besieged, and the self-defense is the right of the occupier.”

The official called this “a huge manifestation of double standards that we will not allow.”

He argued that there was “no comparison” between the level of force used by both sides, and that the Western media had wrongly adopted Israel’s use of the term “rockets” to describe Hamas missiles that were better described as primitive “projectiles.” And he compared the Israeli killing of the top Hamas military official, Ahmed al-Jabari, which in Hamas’s view started the battle, to a hypothetical assassination of Israel’s defense minister, Ehud Barak. “What would be the reaction of the Israelis? Then can you understand the reaction of the other side?”

Echoing an account presented by President Morsi, the Egyptian official said that Israel’s killing of Mr. Jabari had broken an Egyptian-brokered cease-fire agreement that both sides had accepted the day before Mr. Jabari was targeted.

Election regulators named Mohamed Morsi of the Muslim Brotherhood the winner of Egypt’s first competitive presidential elections, handing the Islamist group a symbolic triumph and a new weapon in its struggle for power with the ruling military council.

After an hourlong speech in which he detailed dozens of specific inquiries down to the ballot-box level, the chairman of the election commission, Farouk Sultan, announced that Mr. Morsi had won 51.7 percent of the runoff vote completed last weekend. The other candidate, the former general Ahmed Shafik, won 48.3 percent.

In Tahrir Square, where hundreds of thousands had gathered to await the result, the confirmation of Mr. Morsi’s win brought instant, rollicking celebration. Fireworks went up over the crowd, which took up a pulsing, deafening chant: “Morsi! Morsi!”

Mr. Morsi now becomes the first Islamist elected to be head of an Arab state. But his victory is an ambiguous milestone in Egypt’s promised transition to democracy after the ouster 16 months ago of President Hosni Mubarak.

After an election that international monitors called credible, the military-led government has recognized an electoral victory by an opponent of military rule over Mr. Shafik, who promised harmony with the Supreme Council of the Armed Forces. But Mr. Morsi’s recognition as president does little to resolve the larger standoff between the generals and the Brotherhood over the balance of power over the institutions of government and the future constitution. Under the generals’ plan, Mr. Morsi, 60, will assume an office stripped of almost all authority under a military-issued interim constitution.

Having dissolved the democratically elected and Brotherhood-led Parliament on the eve of the presidential vote, the generals who seized control after Mr. Mubarak’s ouster abrogated their pledge to hand power by June 30, eliciting charges of a new military coup.

After 84 years as an often outlawed secret society struggling in the prisons and shadows of monarchs and dictators, the Brotherhood is now closer than ever to its dream of building a novel Islamist democracy. And its leaders vowed to fight on for the restoration of Parliament regardless of Mr. Morsi’s win.

The mayhem also focused renewed attention on the potential savagery of organized groups of die-hard fans, known here as ultras, who have emerged as a volatile component of Egyptian politics in the year of turmoil since Mr. Mubarak left power.

Previously apolitical, the ultras were known for their rowdy behavior, obscene chants and apparently endless enthusiasm for clashes with the often-brutal Egyptian police. “ACAB,” one group of Cairo ultras likes to spray-paint on city walls, standing for, “All Cops are Bastards.”

The ultras joined the revolt against Mr. Mubarak on the first day of protests, taunting and harassing police as they tried to crack down on thousands of other marchers heading for the Cairo’s Tahrir Square. Protest organizers said they played a more central role in the so-called “battle of the camels,” helping beat back mobs of Mubarak supporters, some of them riding camels, in a daylong battle of rocks and Molotov cocktails.

Since then, however, the ultras have injected an unpredictable element of chaos into the frequent demonstrations over the course of the political transition here. They drove an assault on the Israeli Embassy that triggered a crisis in relations between the two countries last fall. They joined a weeklong battle with security forces near Tahrir Square that left more than 40 dead in November, and another outburst of street fighting near the cabinet building in which more than 15 people died in December.