Jan. 4, 2009 -- Israeli ground forces solidified their hold on the Gaza Strip Sunday, claiming to strike Hamas bunkers and dozens of fighters, and establishing multiple security cordons in an attempt to cut off the movement of Hamas weapons and personnel.
But Israel also suffered its first combat death. ABC News learned the soldier was in the infantry engaged in a heavy firefight on the north end of Gaza. He was killed by mortar fire.
Under cover of artillery and aircraft, Israeli soldiers and tanks entered the narrow strip of land from several directions starting around 7 p.m. local time on Saturday. They entered from the north as well as the east, reaching the sea and cutting the Gaza Strip in two. Another column entered in the south near the Egyptian border.
There were reports of heavy fighting in some areas. Throughout the night, Israeli and Hamas television showed pictures of large explosions inside Gaza, artillery bursts and grainy nightscope video of long lines of Israeli troops moving into the area.
Israeli shelling continued Sunday with artillery shells from the ground and missiles from above. A fuel depot near Gaza City burned all day.
Dozens of Palestinians in Gaza have been killed since the ground operation began Saturday evening, according to the Palestinians. Since the Israeli offensive began nine days ago, more than 500 Palestinians have been killed and more than 2,400 people injured.
Local television reported that five of the Palestinian dead in the ground fighting were civilians killed by an Israeli tank shell at a Gaza City market and another 11 civilians died when a tank shell hit a home north of Gaza City.
In addition to the Israeli fatality, at least 34 other soldiers have been injured since ground operations began.
It appeared this morning that Israeli soldiers had not moved into the most heavily populated areas of Gaza but rather were taking control of key routes and infrastructure.
'A Hard Blow Against Hamas'
Israeli military sources told ABC News the overarching goal of the campaign in the Gaza Strip is to strike "a hard blow against Hamas" and to force the organization into a more amenable negotiating position "to bring about a more stable security situation for its citizens in the south."
The Israeli offensive may already be paying dividends. At a Cabinet meeting today, Yuval Diskin, the head of Israel's security service, Shin Bet, told government officials that Hamas had eased its demands on a cease-fire, according to the newspaper Haaretz.
Even so, international pressure for a cease-fire persisted -- though on ABC News' "This Week With George Stephanopoulos" today, Israeli President Shimon Peres rejected the idea, perhaps a sign from Israel's leadership that the fighting is far from over.
"If there is somebody [who] can stop terror with a different strategy, we shall accept it," Peres said. "We shall not accept the idea that Hamas will continue to fire [rockets at Israel] and we shall declare a cease-fire. It does not make any sense."
Protests and Calls for a Cease-Fire
On Saturday, United Nations Secretary-General Ban Ki-Moon expressed strong reservations about the Israeli ground operation. After speaking to Israeli Prime Minister Ehud Olmert, Ban released a statement saying he "conveyed his extreme concern and disappointment."
The secretary-general also said he is "convinced and alarmed that this escalation will inevitably increase the already heavy suffering of the affected civilian populations."
Today, he added in a new statement, "Given the crucial juncture at which we have arrived in the search for a cease-fire, I appeal to all members of the international community to display the unity and commitment required to bring this escalating crisis to an end. "
Worldwide protests also have demanded an end to Israel's offensive.
In the West Bank today, an Israeli solider shot and killed a 22-year-old Palestinian man violently protesting by throwing rocks.
In Ramallah in the West Bank, a couple thousand Palestinians took to the streets in protest of the Israeli ground operation.
In Istanbul, Turkey, and Rabat, Morocco, enormous peaceful protests brought hundreds of thousands demonstrators onto the streets.
In London, where on Saturday thousands of anti-war protesters hurled shoes at the British Parliament building and at the entrance to Number 10 Downing Street, the prime minister's official residence, British Prime Minster Gordon Brown called the Israeli ground invasion "an escalation" and renewed his call for an immediate cease-fire in a BBC Radio interview.
"This is a very dangerous moment" said Brown. "This is a moment where all the hopes of the peace process are falling apart in the action that's being taken. So what we need is an immediate cease-fire."
Israel says the specific impetus for the offensive is to remove Hamas' ability to fire rockets and mortars at Israeli civilian targets. Since Israeli troops moved in, Hamas has fired 24 rockets and mortars into southern Israeli cities. One rocket injured a woman in Sderot after it scored a direct hit on her home.
Since last Saturday, 500 rockets and mortars have killed four Israelis and injured at least 73 others. Since August 2005, when Israel relinquished control of Gaza, the Israeli military says 6,500 rockets and mortars have been fired into southern Israel.
Despite Israel's ground onslaught, Hamas continued to fire rockets back at Israel -- more than 40 rockets today -- with one destroying a house in the town of Sderot and one giving an American delegation from New York City a brief scare.
New York Mayor Michael Bloomberg, Rep. Gary Ackerman, D-N.Y., and New York Police Commissioner Ray Kelly were in southern Israel on an official visit when rocket alarms sounded twice. None of them was injured.
Eye on Hezbollah
Israel also is keeping its eye on its northern border.
"While we are fighting in Gaza, we keep an open eye on the sensitive situation on our northern border," Defense Minister Ehud Barak said in a televised speech Saturday. "We hope the situation will remain calm. Nevertheless, we are ready and alert to face any unwarranted development in that area."
Barak was addressing a possible offensive by Hezbollah as Israel conducts its ground invasion against Hamas. He is trying to head off what happened in 2006, when Israeli ground forces entered Gaza in an effort to free captured Israeli soldier Gilad Shalit.
Two weeks after Israel moved into Gaza, Hezbollah raided Israel's northern border with Lebanon, killing four soldiers and taking two others hostage. What followed was a major 33-day Israeli offensive into Lebanon which most Israelis feel was lost, despite their inflicting heavy casualties and destruction.
Israel is most concerned with Hezbollah, which enjoys strong support from the Iranian government, Israel's largest, most ardent foe. As Israeli forces were poised to move into Gaza there were a whirlwind of meetings and discussions among Iran, Hezbollah and other anti-Israel entities.
Over the weekend, Saeed Jalili, head of Iran's National Security Council, met with Hezbollah leader Hassan Nasrallah in Beirut, Lebanon, and Hamas political chief Khaled Mashaal in Damascus, Syria.
An Israeli political analyst who did not want to be identified said the meetings in and of themselves indicate that Iran may be trying to more closely coordinate future activities with Hezbollah and Hamas, but the analyst didn't think that they constituted a specific threat tied to the Israeli invasion of Gaza.
"Hamas has become more of an Iranian client," said the analyst, adding that if one looks at the meetings in this context, it "starts to make sense."
ABC News' Simon McGregor-Wood contributed to this story from the Israel-Gaza border. Sami Zyara contributed from Gaza. Bruno Nota, Nasser Atta, Dana Savir, Mimi Daher, Hiba Hajyahye and Michal Mentch-Gerstler contributed to this story from Jerusalem.