GAZA — Israeli troops advanced into Gaza on Sunday under cover of heavy air, tank and artillery fire after opening a ground war against the militant group Hamas on Saturday night.

Witnesses said the Israeli forces had punched across Gaza, bisecting its northern and southern parts, and had taken over certain strategic areas, including what the military has described as rocket launching sites.

The ground campaign came after a week of intense airstrikes. Israel’s stated goal was to destroy the infrastructure of Hamas, the Islamic group that controls Gaza’s government, and to significantly decrease the threat to southern Israel from Palestinian rocket fire.

In a telephone briefing for a group of foreign correspondents, a senior Israeli military official said that Israeli troops would hold the areas they have taken inside Gaza at least for the duration of the operation to prevent militants from returning to fire rockets from there.

“We don’t plan to retake the Gaza Strip but there are several places we control now and will control later,” he said. “If it will be needed, we are prepared to stay there.”

The military has warned that the campaign could take “many long days.”

Even with Israeli forces on the ground, though, Hamas continued its rocket fire. About 25 rockets were launched at southern Israel by Sunday afternoon, the military said. One hit a house in the Israeli border town of Sderot. Touring the town some time later, Michael R. Bloomberg, the mayor of New York, had to be rushed into a protected space when Sderot’s incoming rocket alert sounded.

Most of the fighting early Sunday was taking place in northern and eastern Gaza, in areas not far from the Israeli border. But at least five civilians were killed and many wounded on Sunday morning when Israeli shells or rockets landed in the market of Gaza City while people were stocking up on supplies.

The Israeli military said that they had “hit” dozens of armed Hamas operatives during exchanges of fire overnight. But Palestinian hospital officials said that only about six Hamas fighters had been killed since the start of the ground invasion, a figure that could not be confirmed. Hospital officials said that more than 30 civilians had been killed by Sunday afternoon and more than 100 wounded since Israeli troops had begun advancing.

The Israeli military said that 30 soldiers had been wounded, two seriously, in clashes and from shrapnel.

The senior military official said that Hamas was using methods “imported from Iran and Hezbollah,” the Lebanese militant group. Those methods, he said, were “guerrilla concept and tactics, exploiting both open areas and those of highest density of population.” He said there had not been much man-to-man combat so far, and that Hamas was fighting back mostly with mortars and improvised explosive devices, or I.E.D.s.

Wounded civilians poured into the emergency room of Shifa Hospital in Gaza City on Sunday, including women and children. Two young cousins and a 5-year-old boy from another family were killed by shrapnel as they played on the flat roofs of their apartment buildings, after having been cooped up inside for long hours.

A woman who came to the hospital with a daughter, 15, who was wounded by shrapnel, said that soldiers had taken over their house in Beit Lahiya, had detained the men, who she said were farmers, and told the rest of the family to leave. The daughter was injured when the Israeli forces fired on the upper floors of the house before breaking the front door down.

Condemnation for the Israeli offensive grew across the Middle East.

Egyptian Foreign Minister Ahmed Abul Gheit said Israel’s incursion into Gaza came in “brazen defiance” of international calls to end the offensive, according to Agence France-Presse.

“The Security Council’s silence and its failure to take a decision to stop Israel’s aggression since it began was interpreted by Israel as a green light,” he said in a statement.

A State Department official said Saturday the United States was working toward a cease-fire, according to the Associated Press. But the White House has blamed Hamas for the escalating violence and blocked approval of a United Nations Security Council statement on a cease-fire.

The Israeli ground assault brings new risks and the prospect of many new casualties on both sides in a confrontation that, before this phase began late Saturday, had already cost the lives of more than 430 Palestinians and 4 Israelis.

While a ground war in densely populated Gaza is likely to increase the civilian toll there, the Israeli Army also faces new threats. Since seizing control of the territory a year and a half ago, Hamas has been able to smuggle in more and better weapons. Its more sophisticated arsenal has been on display in recent weeks, and even under heavy fire the group has shown its ability to keep hitting Israeli cities with long-range rockets.

Rockets fired from Gaza have plagued southern Israel for years, and they have drawn the military into the coastal territory repeatedly since troops formally withdrew and the Jewish settlements there were evacuated in 2005. A 48-hour raid in March 2008, aimed at inflicting a cost on Hamas for its continuing rocket fire, killed nearly 100 Palestinians.

Israeli officials have said repeatedly that it is not their aim now to fully reoccupy Gaza. But it was clear that the military expected a grueling operation.

“This will not be easy and it will not be short,” Defense Minister Ehud Barak said on national television shortly after the ground invasion began. He did not elaborate on how long Israel hoped to hold the rocket-launching sites.

The ground operation began after eight days of intensive attacks by Israeli air and naval forces on Hamas security installations, weapons stores and symbols of government in the Palestinian enclave.

“This has always been a stage-by-stage process,” Shlomo Dror, a Defense Ministry spokesman, said in a telephone interview. “Hamas can stop it whenever it wants,” by stopping its rocket fire, he said.

Hamas leaders in Gaza were in hiding, but a Hamas spokesman said Saturday night by video that the “moment of decision has arrived” and that Gaza would be the Israeli Army’s “graveyard.”

Hamas has also threatened to use the invasion as an opportunity to capture Israeli soldiers. The group has been holding an Israeli corporal, Gilad Shalit, hostage for more than two years.

The exact number of troops entering Gaza was not being publicized, but the military said the operation involved “large numbers” of forces including infantry, tanks, engineering and artillery corps. On Saturday night, the Israeli prime minister’s office said that a call-up of thousands of army reserve troops, approved earlier, had begun.

Before Israel started the invasion, warplanes and ground artillery carried out heavy strikes on Saturday. Many of those attacks were on open areas around Beit Hanoun and the main route connecting the north and south of Gaza, most likely to clear those areas of mines and tunnels and to hamper movement before troops entered.

A mosque in northern Gaza was also hit, during evening prayer time, in what witnesses said was an Israeli airstrike. At least 11 worshipers were killed and about 30 wounded, according to Palestinian hospital officials. The Israeli military had no immediate comment.

The air force has struck several mosques in the past week, with the military saying they served as Hamas bases and weapons stores.

The Israeli Army also dropped thousands of leaflets into some residential districts warning inhabitants to evacuate their homes. Because of “the activity of terrorist groups,” the leaflets said in Arabic, the army “is obliged to respond quickly and work from inside your residential area.” Many residents of one apartment block in Gaza City said they had nowhere else to go and would stay in their homes.

An Egyptian-brokered truce between Israel and Hamas, which took effect last June, began to break down in November, and Hamas declared it over on Dec. 19. Since then, rocket fire out of Gaza has intensified.

On Saturday, a rocket hit an apartment building in the major port city of Ashdod, about 20 miles north of Gaza, lightly wounding two Israelis. Other rockets landed in the coastal city of Ashkelon and in the Negev Desert town of Netivot.

The latest round of rocket fire has demonstrated the extent to which Hamas has been able to upgrade its arsenal with weapons parts smuggled into Gaza, according to American and Israeli officials. Compared with the crude, homemade Qassam rockets it had used in the past, the latest rockets have been more accurate and have flown farther — close to two dozen miles, enough to reach the southern Israeli cities of Ashdod and Beersheba.

President Bush, in his weekly radio address to the nation on Saturday, said Hamas had instigated the violence last week with rocket barrages “that deliberately targeted innocent Israelis.”

Expressing concern about the humanitarian situation facing the people of Gaza, he added that the United States was “leading diplomatic efforts to achieve a meaningful cease-fire that is fully respected.”

President-elect Barack Obama continued to defer publicly to the Bush administration after the ground campaign began. “The president-elect is closely monitoring global events, including the situation in Gaza,” said Brooke Anderson, his chief national security spokeswoman. “There is one president at a time, and we intend to respect that.”

The United Nations Security Council held a closed meeting, called by France, on Saturday. Earlier, Secretary General Ban Ki-moon called for “an immediate end” to Israel’s ground operation, and asked Israel to “ensure the protection of civilians and that humanitarian assistance is able to reach those in need.”

Before the ground war began, hospital officials in Gaza City put the first week’s Palestinian death toll at more than 430, including 26 women, 74 children and an unknown number of male civilians. Three Israeli civilians and one soldier had been killed by rocket fire.

World reaction was intense and mixed. While thousands of protesters marched in cities across Europe to demand a halt to the Israeli bombing, in Prague, a spokesman for the new Czech presidency of the European Union said Israel’s actions were “defensive, not offensive.”

Other European countries quickly distanced themselves from the Czech position. The French Foreign Ministry condemned “the Israeli ground offensive against Gaza as it condemns the continuation of rocket firing.”

In London, the British foreign secretary, David Miliband, urged both sides to accept an immediate cease-fire.

More than 20,000 demonstrators marched against the Israeli air campaign in Paris and more than 10,000 in London, where some threw shoes at the prime minister’s residence, a particularly Arab form of protest that has gained worldwide currency since an Iraqi journalist hurled his shoes at President Bush last month in Baghdad.

Both protests were held before the ground invasion began. Large protests also took place in at least seven other European countries and in Kuwait, Israel and New York.

The Israeli military said Saturday evening that the air force had struck about 40 Hamas targets during the day, including weapons storage facilities, smuggling tunnels, rocket launchers and launching sites. Palestinians said the airstrikes also hit the American International School, a private institution in northern Gaza, killing a school guard.

Israel has also been firing on the homes of Hamas’s military leaders, and on Saturday struck a vehicle in Khan Yunis carrying Mohammed Maaruf, whom the Israeli military described as an officer in the Hamas ground forces. Another strike killed Mohammad al-Jammal, 40, who was said in Gaza to be a Hamas military commander, according to the news service Agence France-Presse. Israel said he was responsible for the entire rocket-launching operation in all of Gaza City.