KIRYAT MALACHI, Israel — Israel and Hamas widened their increasingly deadly conflict over Gaza on Thursday, as a militant rocket killed three civilians in an apartment block in this small southern town. The deaths are likely to lead Israel to intensify its military offensive on Gaza, now in its second day of airstrikes.

In Gaza, the Palestinian death toll rose to 11 as Israel struck what the military described as medium- and long-range rocket and infrastructure sites and rocket-launching squads. The military said it had dispersed leaflets over Gaza warning residents to stay away from Hamas operatives and facilities, suggesting that more was to come.

The regional perils of the situation sharpened, meanwhile, as President Mohamed Morsi of Egypt warned on Thursday that his country stood by the Palestinians against what he termed Israeli aggression, echoing similar condemnation on Wednesday.

“The Egyptian people, the Egyptian leadership, the Egyptian government, and all of Egypt is standing with all its resources to stop this assault, to prevent the killing and the bloodshed of Palestinians,” Mr. Morsi said in nationally televised remarks before a crisis meeting of senior ministers. He also said he had contacted President Obama to discuss strategies to “stop these acts and doings and the bloodshed and aggression.”

In language that reflected the upheaval in the political dynamics of the Middle East since the overthrow of Hosni Mubarak last year, Mr. Morsi said: “Israelis must realize that we don’t accept this aggression and it could only lead to instability in the region and has a major negative impact on stability and security in the region.”

The thrust of Mr. Morsi’s words seemed confined to diplomatic maneuvers, including calls to the United Nations secretary general, Ban Ki-moon, the head of the Arab League and President Obama.

In his conversation with Mr. Obama, Mr. Morsi said, he “clarified Egypt’s role and Egypt’s position; our care for the relations with the United States of America and the world; and at the same time our complete rejection of this assault and our rejection of these actions, of the bloodshed, and of the siege on Palestinians and their suffering.”

Mr. Obama had agreed to speak with Israeli leaders, Mr. Morsi said. Thursday’s deaths in Kiryat Malachi were the first casualties on the Israeli side since Israel launched its assault on Gaza, the most ferocious in four years, in response to persistent Palestinian rocket fire.

Southern Israel has been struck by more than 750 rockets fired from Gaza this year that have hit homes and caused injuries. On Thursday, a rocket smashed into the top floor of an apartment building in Kiryat Malachi, about 15 miles north of Gaza. Two women and a man were killed, according to rescue officials and Army Radio. A baby was among the injured and several Israelis were hospitalized with shrapnel wounds after rockets hit other southern cities and towns, they said.

The apartment house was close to a field in a blue-collar neighborhood and the rocket tore open top-floor apartments, leaving twisted metal window frames and bloodstains.

Nava Chayoun, 40, who lives on the second floor, said her husband, Yitzhak, ran up the stairs immediately after the rocket struck and saw the body of a woman on the floor. He rescued two children from the same apartment and afterward, she said, she and her family “read psalms.”

It was the first time that a building in Kiryat Malachi had been struck and the farthest north a projectile had landed in the current violence. With schools closed after Wednesday’s turmoil, residents said, many people had stayed home with their children.

Residents said people living on the lower floors of the apartment house had taken cover in stairwells, as the police urged residents to do when they heard warning sirens, but those on the top floor apparently had not. The police said 180 rockets had been fired at southern Israel since Wednesday.

In Gaza, three militants were killed when Israeli missiles hit their motorcycles in the southern Gaza town of Khan Younis. Palestinian security officials said they were most likely members of the Hamas military wing. Overnight, the body of a man, 65, was recovered from an open area that had been struck in the center of the Gaza Strip.

Five other civilians, including a baby and a 7-year-old girl, have been killed in Gaza since the operation began and at least 70 have been wounded, according to the Hamas-run Health Ministry in Gaza.

The Israeli offensive has damaged Israel’s fragile relations with Egypt and escalated the risks of a new war in the Middle East.

It opened on Wednesday with the killing of the top military commander of Hamas, Ahmed al-Jabari, who was killed in an airstrike as he was riding in a car. The Israelis have warned all Hamas leaders in Gaza to stay out of sight or risk the same fate.

On Thursday, hundreds of people took part in Mr. Jabari’s funeral, but Hamas leaders did not attend. As the procession wound its way through the streets from Mr. Jabari’s home to a mosque, the participants sometimes broke into a jog as Israeli warplanes dropped bombs nearby. Shops were closed in Gaza, and the streets were empty.

Outside the Al-Omari mosque, Wael Jabari, 35, cried. Last year he was freed after spending 11 years in an Israeli prison, in a deal brokered by Egypt that also secured the release of an Israeli soldier, Gilad Shalit. Mr. Jabari, who was Mr. Jabari’s uncle by marriage, represented Hamas in the negotiations. “His insistence made the swap successful,” Mr. Jabari said.

In an address to mourners in the mosque, Mushier al-Massri, a Hamas lawmaker, promised a “devastating” response. “The resistance is able to force the occupation to pay the price of its crimes,” he said.

The Israel Defense Forces coupled the intense airstrikes with the threat of a ground invasion of Gaza, recalling its three-week operation in the winter of 2008-9, shifting infantry brigades and calling up some specialist reserves. “We recommend that no Hamas operatives, whether low level or senior leaders, show their faces above ground in the days ahead,” the Israel Defense Forces said in a Twitter message. Brig. Gen. Yoav Mordechai, the military spokesman, said, “If I were a senior Hamas activist, I would look for a place to hide.”

The escalation in hostilities between Israel and Hamas, the militant organization regarded by Israel as a terrorist group sworn to its destruction, prompted Egypt to recall its ambassador on Wednesday and demand meetings of the United Nations Security Council and the Arab League. Israel had already been facing growing tensions with its Arab neighbors. It has confronted lawlessness on its frontier with Egypt in the Sinai Peninsula, including cross-border attacks. In the last week, the military twice fired into Syria, which is engulfed in a civil war, after mortar rounds fell in the Israeli-occupied Golan Heights.

On Saturday, Gaza militants fired an antitank missile at an Israeli military jeep patrolling the Gaza border, injuring four soldiers.

Both the rocket fire and the buildup of advanced weaponry in Gaza have increasingly tested Israeli officials and prompted such an intense response, according to military experts in Israel.

The ferocity of the airstrikes provoked rage in Gaza, where Hamas said the campaign amounted to war. It quickly launched dozens of rockets into the south but Israel’s Iron Dome anti-rocket defense system intercepted many of them high above the ground.

Civil defense authorities in Israel, anticipating retaliation, had instructed residents within a 25-mile radius of Gaza not to go to school or work on Thursday. Many remained indoors or congregated in bomb shelters.

General Mordechai said the operation “would continue and grow.” The military said it was designed to “severely impair the command and control chain of the Hamas leadership.”

By targeting Mr. Jabari, 52, the Israelis said they had killed the mastermind of virtually every attack to come from Gaza in recent years, including the kidnapping in 2006 of Mr. Shalit, then a corporal. Mr. Shalit’s five years as a prisoner marked a period of national anguish and when he was finally released through Egypt, Mr. Jabari made a rare public appearance alongside him.

The attacks on Gaza have been undertaken at a delicate time for Prime Minister Benjamin Netanyahu of Israel, nine weeks before elections, and may have partly reflected his administration’s own sense that it needed to send a message of deterrence beyond Gaza. In a statement, Mr. Netanyahu praised the military for the operation and said: “We will not accept a situation in which Israeli citizens are threatened by the terror of rockets. No country would accept this.”

In Washington, the White House issued a carefully worded statement saying President Obama had spoken with both Mr. Netanyahu and President Morsi of Egypt, reiterating to both that the United States supports Israel’s right to self-defense from the rocket attacks. The statement said Mr. Obama had urged Mr. Netanyahu to “make every effort to avoid civilian casualties,” and that Mr. Obama and Mr. Morsi “had agreed on the importance of working to de-escalate the situation as quickly as possible.”

Nonetheless, the Israeli attacks further complicated Israel’s fragile relations with Egypt, where the Islamist-led government of Mr. Morsi, reversing a policy of Mr. Mubarak’s, had established closer ties with Hamas and had been acting as a mediator to restore calm between Israel and militant groups in Gaza.

In the first crisis in Israeli-Egyptian relations since Mr. Morsi came to power, he called the Israeli actions “wanton aggression on the Gaza Strip” in justifying his decision to summon home the ambassador.

Mr. Morsi’s Freedom and Justice Party, rooted in the same Muslim Brotherhood origins as Hamas, posted a video on its Web site of what was described as the burned body of a Palestinian child said to have been killed in the Israeli attacks, in an attempt to stoke anger at Israel. His party also issued a statement saying: “The wanton aggression against Gaza proves that Israel has yet to realize that Egypt has changed and that the Egyptian people who revolted against oppression will not accept assaulting Gaza.”The Israel Defense Forces said Mr. Jabari had been targeted because he “served in the upper echelon of the Hamas command and was directly responsible for executing terror attacks against the state of Israel in the past number of years.”

Mr. Jabari led Hamas forces when they took control of Gaza in 2007, ousting the rival Palestinian faction Fatah and the Palestinian Authority two years after the Israelis withdrew from the territory which was captured in the 1967 war.

Israeli forces went back into Gaza in the winter of 2008-9 after years of rocket attacks by Palestinian militants into Israel. The Israeli invasion killed as many as 1,400 Palestinians, including hundreds of civilians, and was widely condemned internationally.

Since then, Hamas has mostly adhered to an informal, if shaky, cease-fire and at times tried to force smaller militant groups to stick to it, too. But in recent months, under pressure from some of the Gaza population for not avenging deadly Israeli airstrikes, Hamas has claimed responsibility for participating in the firing of rockets.