Israeli ground forces battled Hamas after crossing into the Gaza Strip from several directions Saturday evening, an escalation of an offensive intended to stop the militant group from launching rocket attacks against Israel.
"It will not be easy or short, but we are determined," Israeli Defense Minister Ehud Barak told reporters shortly after troops and tanks moved in.
"We are peace-seekers," Barak added. "We have restrained ourselves for a long time. But now is the time to do what needs to be done."
Around the same time, Hamas spokesman Ismail Radwan said in a television appearance that Israel was falling into a Hamas trap and vowed that Hamas would fight until defeating Israeli forces.
"Gaza will not be a picnic," a Reuters translation quoted Radwan as telling the Israelis. "Gaza will be a graveyard for you."
Both Palestinians and Israelis reported intense fighting.
Early on, Hamas claimed it had killed Israeli soldiers, though Israeli officials denied that claim.
In the first four hours of the ground invasion, there were 20 Palestinian deaths, a Palestinian medical official from the Shifa Hospital in Gaza told ABC News.
Even before troops moved in, a weeklong air assault on Hamas already had claimed the lives of more than 440 Palestinians. At least four Israelis have been killed as Hamas fired more than 400 rockets and mortars into Israel.
President George W. Bush and President-elect Barack Obama continue to be briefed on the escalating situation in Gaza. The Bush administration has so far blamed Hamas for the crisis, saying it must stop the rockets into Israel.
This evening, a statement by State Department spokesman Sean McCormack said the United States has advised Israel "to be mindful of the potential consequences to civilians" and is working toward a cease-fire that would not allow Hamas to launch rockets.
"Hamas has held the people of Gaza hostage ever since their illegal coup against the forces of President Mahmoud Abbas, the legitimate president of the Palestinian people," McCormack said. "They have used Gaza as a launching pad for rockets against Israeli cities, and have contributed deeply to a very bad daily life for the Palestinian people in Gaza and to a humanitarian situation that we have all been trying to address. Hamas has made it very difficult for the people of Gaza to have a reasonable life."
U.N. Secretary-General Ban Ki-Moon was more critical of Israel for its escalation, and he conveyed "extreme concern and disappointment" to Israeli Prime Minister Ehud Olmert, a statement from his office said.
"He is convinced and alarmed that this escalation will inevitably increase the already heavy suffering of the affected civilian populations," the statement added. "He called for an immediate end to the ground operation, and asked that Israel do all possible to ensure the protection of civilians and that humanitarian assistance is able to reach those in need."
Israel: 'Destroy the Terrorist Infrastructure'
Israeli officials said the ground offensive was the second stage of its "Operation Cast Lead" -- meant to hobble Hamas and to increase the "deterrent strength" of the Israeli Defense Forces.
"The objective of this stage is to destroy the terrorist infrastructure of the Hamas in the area of operation," an IDF statement said, "while taking control of some of rocket launching area used by the Hamas, in order to greatly reduce the quantity of rockets fired at Israel and Israeli civilians."
To achieve those goals, Israel attacked the tiny Gaza Strip from four directions on land and, possibly, by sea. Sources told ABC News the plan was to encircle Gaza City, Gaza's biggest population center with 250,000 people, by morning.
Israeli forces aimed essentially to cut the Gaza Strip into four slices, to go after almost 300 Hamas concrete tunnels and defensive installations, and to try to draw Hamas fighters onto the streets where they'd be more vulnerable, ABC News' Simon McGregor-Wood reported.
The Israeli government also authorized the call up of thousands of reservists, signaling that the conflict could widen even more.
Israelis Head Into 'a Barrel of Explosives'
Israeli officials said the country's forces did not intend to reoccupy the Gaza Strip, which its forces occupied until 2005.
"We think it's gonna be a long operation," said Maj. Avital Leibovich, an Israeli military spokesman. "This is due to the fact that Hamas, for the past two years, has invested a lot of time and effort in turning Gaza into a barrel of explosives."
Israeli forces have gone into Gaza at least twice before since pulling out in 2005 -- including a fairly large maneuver in 2006 and a smaller one 10 months ago.
Barak noted Israel also was keeping "an open eye on the sensitive situation on our northern border" with Lebanon, where Israel fought a battle against Hezbollah in 2006, vowing to stop the group's missile-launching capabilities. In that case, even after Israeli troops invaded Lebanon, Hezbollah launched an increasing number of missiles at Israel.
This time, the IDF statement suggested Israeli forces were entering the much smaller Gaza Strip with formidable force.
"Large numbers of forces are taking part in this stage of the operation, including infantry, tanks, engineering forces, artillery and intelligence with the support of the Israel Air Force, Israel Navy, Israel Security Agency and other security agencies," the statement said.
"The residents of Gaza are not the target of the operation," the statement added. "Those who use civilians, the elderly, women and children as 'human shields' are responsible for any and all injury to the civilian population. Anyone who hides a terrorist or weapons in his house is considered a terrorist."
Earlier Saturday, at least 10 people were killed in an Israeli air strike on a mosque in northern Gaza, Palestinian medical officials told the Associated Press.
It was not immediately clear whether those killed in the mosque attack in the northern town of Beit Lahiya were militants or civilians.
In a separate attack, the Israeli army claims to have killed Abu Zakaria al-Jamal, the latest senior Hamas leader to have perished since the attacks began eight days ago.
According to the United Nations, Israeli forces have hit 600 targets since the air strikes began.
The beginning of artillery attacks Saturday before the ground invasion raised the possibility of additional civilian casualties caused by the relative inaccuracy of artillery shells compared with precision missile strikes, according to an AP report.
'No Place to Hide'
Before the ground attack, Israel allowed some 300 Palestinians who hold dual citizenship to leave the heavily bombed region of over 1 million residents Friday after pleas from other governments that they be permitted to leave.
"There is no place to hide," Palestinian-American Jawahir Haggi told ABC News. "You want to go to a house, do you want to go and hide? You find bombs and the Israelians [sic]. You go to another house, you find bomb and Israelians [sic]. There is no place to hide."
According to U.N. reports, some aid is getting through, but not enough to cope with the massive demands the conflict has placed on food resources, hospitals and utilities.
Many civilians have not survived long enough to feel the aid shortage.
The U.N. estimated Friday that a quarter of the Palestinians killed in air strikes were civilians.
"They are supposed to destroy just the Hamas, but people in their homes are dying too," Hajji, a 14-year-old U.S. citizen, told the AP.
On Monday, Israeli Foreign Minister Tzipi Livni told reporters the military was targetting only Hamas and that Hamas "hides among civilians."
Thursday, Israeli air strikes killed senior Hamas leader Nizar Rayyan. His four wives and 11 children were also killed by the 2,000 pound bomb.
International Anger at Israel
The ground invasion began on a day of protest throughout Europe against Israel's offensive in Gaza -- with demostrators turning out in Paris, Berlin, Athens, Rome and 18 cities in Great Britain.
Up to 12,000 people gathered in London's Trafalgar Square, where protestors expressed anger at what they saw as a disproportionate response by the Israelis, ABC News Radio's Tom Rivers reported.
"Killing 100 Arabs for every Jew that is killed is not proportionate," Former London Mayor Ken Livingstone told the crowd. "It is a war crime."
Livingstone said he hoped the demonstration would send a powerful message to British Prime Minister Gordon Brown, and he said he described the silence of most Western governments to the Israeli attacks as obscene.
ABC News' Simon McGregor-Wood, Mimi Daher, Tom Rivers and Tom McCarthy contributed to this report.