Israel launched the operation late Thursday, following a 10-day campaign of more than 2,000 air strikes against Gaza that had failed to halt relentless Hamas rocket fire on Israeli cities.
Israel's first major ground offensive in Gaza in just over five years came as Egyptian cease-fire efforts stalled. Earlier this week, Israel accepted Cairo's offer to halt hostilities, but Hamas refused, demanding that Israel and Egypt first give guarantees to ease the blockade on Gaza.
Israeli Prime Minister Benjamin Netanyahu said he had ordered the military to prepare for a "significant expansion" of the ground offensive.
"It is not possible to deal with tunnels only from the air. It needs to be done also from the ground," he said before a special Cabinet meeting in Tel Aviv.
"We chose to begin this operation after the other options were exhausted and with the understanding that without the operation the price we will pay can be very high."
Throughout the night, the thud of tank shells echoed across Gaza, often just a few seconds apart. Several explosions from Israeli missile strikes shook high-rise buildings in central Gaza City. Pillars of smoke could be seen from the Israeli side of the border.
At Gaza's main Shifa Hospital, casualties quickly began arriving, including several members of the same family wounded by shrapnel from tank shells. Among those hurt were a toddler and a boy of elementary school age, their bodies pocked by small bloody wounds.
Gaza health officials said at least 20 Palestinians have been killed since the ground operation began, including three teenage siblings. The Israeli military said it killed 14 militants in different exchanges of fire. It was not immediately clear if the militants were among those reported killed by Gaza authorities.
"The ground offensive does not scare us and we pledge to drown the occupation army in Gaza mud," Hamas spokesman Sami Abu Zuhri said in a statement.
The Israeli military said one soldier was killed in the northern Gaza Strip, the first Israeli casualty among troops. The circumstances behind the death of Staff Sgt. Eitan Barak, 20, were not immediately clear, with Hamas' military wing saying it ambushed Israeli units in the northern town of Beit Lahiya and caused casualties but Israeli media saying it was likely a case of friendly fire.
Israel's chief military spokesman Brig. Gen. Moti Almoz told Army Radio "there were a number of points of friction through the night" and said the military was investigating the circumstances behind the soldier's death.
Tanks, infantry and engineering forces were operating inside the coastal strip. In a statement, the military said it targeted rocket launchers, tunnels and more than 100 other targets. The military said a number of soldiers were wounded throughout the night.
Israeli officials have said the goal is to weaken Hamas militarily and have not addressed the possibility of driving the Islamic militants from power.
However, Hamas has survived Israeli offensives in the past, including a major ground operation in January 2009 from which it emerged militarily weaker, but then recovered. Hamas has since assembled thousands of rockets and built a system of underground bunkers.
Israel had been reticent about launching a ground offensive for fear of endangering its own soldiers and drawing international condemnation over Palestinian civilian deaths.
Since the July 8 start of the air campaign, more than 260 Palestinians have been killed and more than 2,000 wounded, Palestinian health officials said. In Israel, one civilian died and several were wounded.
Israeli public opinion appears to strongly support the offensive after days of unrelenting rocket fire from Gaza and years of southern Israeli residents living under the threat. Gaza militants have fired more than 1,500 rockets at Israel over the past 11 days.
Israel said it launched an open-ended assault on several fronts, with the primary aim being to destroy underground tunnels into Israel built by Hamas that could be used to carry out attacks.
On Thursday, 13 heavily armed Hamas militants tried to sneak in through such a tunnel, but were stopped by an airstrike after they emerged some 250 meters (820 feet) inside Israel.
Israeli defense officials said soldiers faced little resistance during the first night of the ground operation, but the longer troops remain in Gaza, the greater the risk for heavy casualties on both sides.
Forces are expected to spend a day or two staking out positions and are working in the north, east and south of the Gaza Strip. Then, they are expected to move to the second phase, which is to destroy tunnels, an operation that could take up to two weeks.
Once Hamas is able to study the military's positions and movements, it may push back more forcefully, the officials said.
The officials spoke on condition of anonymity because they were not authorized to discuss the military's strategy.
"The mission is progressing well," said Lt. Gen. Benny Gantz, Israel's military chief. "There were a number of incidents overnight that we overcame and moved forward."
Prior to the Israeli Cabinet meeting, several ministers said they expected a prolonged offensive.
"This operation must be completed to its end and that includes a significant incursion into Gaza," said Uri Ariel, a Cabinet minister from the hardline Jewish Home party.
"We need to go in and finish the job. We need to eliminate every terrorist. They have no immunity."
Goldenberg reported from Jerusalem. Associated Press writer Aron Heller contributed to this report from Jerusalem.
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