JERUSALEM — Diplomatic efforts accelerated on Tuesday to end the deadly confrontation between Israel and Palestinian militants in Gaza, 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.

The diplomatic moves to end the nearly week-old crisis came on a day of some of the most intense violence yet, in what appeared to be efforts by the antagonists to get their last attacks done before a cease-fire went into effect.

Israeli aerial forces assaulted several Gaza targets, including a suspected rocket-launching site near Al Shifa hospital, which killed at least nine people, and Israeli naval vessels launched an intensive shelling aimed at the Gaza coastline. A delegation visiting from the Arab League canceled a news conference at the hospital because of the Israeli aerial assault as wailing ambulances brought victims in, some of them decapitated.

Militants in Gaza fired a barrage of rockets into southern 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.

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.

Foreign diplomats who were briefed on the outlines of a tentative agreement said it had been structured in stages — first, an announcement at approximately 10 p.m. local time (3 p.m. E.S.T.) of a cease-fire, followed by its implementation at midnight, for 48 hours. That would allow time for Mrs. Clinton to arrive, and to create a window for negotiators to agree on conditions for a longer-term cessation of hostilities.

Whether Hamas can enforce control over all of the militant Palestinian factions in Gaza to hold their fire during that period remained unclear.

The announcement of Mrs. Clinton’s active role in efforts to defuse the crisis added a strong new dimension to the multinational push to avert a new Middle East war. Israel has amassed thousands of soldiers on the border with Gaza and has threatened to invade the crowded Palestinian enclave for the second time in four years to stop the persistent rockets that have been lobbed at Israel.

Mrs. Clinton, who accompanied President Obama on his three-country Asia trip, left Cambodia on her own plane immediately for the Middle East. She was en route to Jerusalem to meet with Prime Minister Benjamin Netanyahu of Israel, then head to the West Bank to meet with Palestinian leaders and finally to Cairo to consult with Egyptian officials.

Mr. Obama made a number of late-night phone calls from his Asian tour to the Middle East on Monday night that contributed to his conclusion that he had to become more engaged and that Mrs. Clinton might be able to accomplish something.

With Ban Ki-moon, the United Nations secretary general, also in Israel on Tuesday, a senior official in Prime Minister Benjamin Netanyahu’s office said Israel had decided to give more time to diplomacy before starting a ground invasion into Gaza. But Israel has not withdrawn other options.

“I prefer a diplomatic solution,” Mr. Netanyahu said in a statement at the start of a meeting in Jerusalem with the German foreign minister, Guido Westerwelle. “I hope that we can get one, but if not, we have every right to defend ourselves with other means and we shall use them.

“As you know, we seek a diplomatic unwinding to this, through the discussions of cease-fire,” Mr. Netanyahu added. “But if the firing continues, we will have to take broader action and we won’t hesitate to do so.”

Intensifying the pressure on Hamas after a day of heavy rocket fire out of Gaza against southern Israel, the Israeli military said on Tuesday afternoon that it had distributed leaflets over Gaza instructing the Palestinian residents in several areas to evacuate their homes immediately, “for your safety,” and to move toward defined zones in central Gaza City. That seemed intended to signal that plans for a ground operation were imminent should the cease-fire talks fail. About three hours before Mr. Ban was scheduled to meet Mr. Netanyahu in Jerusalem, sirens sounded across the city in the early afternoon announcing an incoming rocket from Gaza. The military wing of Hamas said it had fired at the city. The rocket fell short, landing harmlessly in the West Bank just south of Jerusalem, and the military said it landed on open ground near a Palestinian village.

The rocket attack on the city, which is holy to Jews, Muslims and Christians, was the second in less than a week. On Friday, a rocket landed in a similar location, the police said.

The Israeli military said its air force had struck Tuesday morning at 11 Palestinian squads involved in planting explosives and firing rockets, as well as underground rocket launchers and a store of weapons and ammunition. The military said it had also used tank shells and artillery fire against unspecified targets in Gaza.

The Health Ministry in Gaza said the Palestinian death toll had climbed by late Tuesday morning to 112, roughly half of the dead civilians, including children. Three Israelis died in a rocket attack last week.

After an Asian summit dinner in Phnom Penh, Cambodia, on Monday night, Mr. Obama called President Morsi to discuss the situation, then spoke with Mr. Netanyahu and called Mr. Morsi back. He was up until 2:30 a.m. on the phone, the White House said. He consulted with Mrs. Clinton repeatedly on the sidelines of the Asian summit meetings on Tuesday.

“This morning, Secretary Clinton and the president spoke again about the situation in Gaza, and they agreed that it makes sense for the secretary to travel to the region, so Secretary Clinton will depart today,” said Benjamin Rhodes, a deputy national security adviser to Mr. Obama. “Her visits will build on the engagement that we’ve undertaken in the last several days.”

Mr. Rhodes said, “Any resolution to this has to include an end to that rocket fire” by Hamas militants on Israeli communities, but “the best way to solve this is through diplomacy.”

He added, “It’s in nobody’s interest to see an escalation of the military conflict.”

Mrs. Clinton will not meet with Hamas representatives on her trip, but with the Palestinian leadership in the West Bank, which is at odds with the Hamas rulers of the Gaza Strip. “We do not engage directly with Hamas,” Mr. Rhodes said. Instead, Mr. Obama is focused on leveraging Egypt’s influence with Hamas to press for a halt to the rocket attacks. “We believe Egypt can and should be a partner in achieving that outcome,” Mr. Rhodes said.

Mr. Rhodes reaffirmed that the United States supports Israel’s right to defend itself and said Mr. Obama had not asked Mr. Netanyahu to hold off a ground incursion into Gaza.

Separately, an Israeli man attacked an Israeli security guard outside the American Embassy in Tel Aviv with an ax and a knife on Tuesday, injuring the guard. The guard fired warning shots, apprehended the assailant and handed him over to the Israeli police, according to a police spokesman who described the episode as a “criminal incident” unrelated to the current security situation.

Mrs. Clinton’s trip comes as she is preparing to step down as secretary of state, presenting her with a delicate late test after four years in which Mr. Obama’s administration has failed to achieve the broader peace it once sought in the region.

With the president’s re-election behind him, Mrs. Clinton plans to resign around the time of the second inauguration on Jan. 20. Aides said she would stay until a successor could be confirmed as long as the confirmation process does not drag too long into the new year.

The abrupt change in plans here underscored the challenges for Mr. Obama as he tries to reorient American foreign policy away from its dominant focus on the Middle East and more toward the Asia-Pacific region. Even as he chose Southeast Asia as the destination for the first overseas trip after winning a second term, Mr. Obama has found himself drawn every day into the deadly dispute consuming the Middle East.