JERUSALEM - Hamas militants engaged in gun battles with Israeli forces and sought to target them with explosive devices on Saturday while continuing to fire rockets into Israel, as the conflict stretched into its 12th day.
In one incident, the militants strapped a donkey with explosives and pushed it in the direction of Israeli soldiers, said Israel's military, adding in a statement that soldiers "engaged the donkey and it exploded at a safe distance" without injuring any troops.
Even as Israeli ground forces targeted Hamas' tunnel networks inside Gaza - their main stated objective - Islamist militants infiltrated Israel early Saturday through a tunnel in central Gaza, Israel's military said.
The Palestinian gunmen, disguised in Israeli uniforms, killed two Israeli soldiers and injured several others, the military said. At least one Palestinian was killed in the clash. The rest of the Palestinian fighters fled back into Gaza, said Israel's military.
The Palestinian death toll from the conflict rose Saturday to nearly 350, with about 2,200 injured, according to the Gaza Health Ministry.
Gaza Health Ministry spokesman Ashraf al-Kidra said the new round of air strikes raised the death toll from the offensive to at least 342 Palestinians, many of them civilians.
In Israel, a rocket fired from Gaza killed a man near the southern city of Dimona and wounded four people, police said, marking the second Israeli civilian casualty from the fighting. An Israeli soldier was killed after the start of the ground operation, probably from friendly fire.
The United Nations estimates that 80 percent of the casualties are civilians, many of them children. Tens of thousands of Palestinians are seeking refuge in U.N. shelters.
Israel's ground forces remained focused around the fringes of Gaza's border, searching for Hamas tunnel networks and rocket launchers, and had not advanced into Gaza's densely populated urban areas by Saturday afternoon, said Capt. Eytan Buchman, an Israeli army spokesman.
Adele Raemer, who lives on a kibbutz near the border, said she received an alert on her phone mid-morning Saturday. "It said because of a suspicion of infiltration, everybody should stay in their homes," said Raemer, who was in the midst of baking bread and dared to put the dough outside on the ledge to rise.
The restrictions eased up around lunchtime but were reinstated around 4 p.m. At that point, Raemer said, she heard machine-gun fire. "When I get these messages, I take them very seriously," said Raemer, a resident of Kibbutz Nirim, about a mile from the border. "The messages are telling me they are preventing someone from entering my kibbutz."
Since the ground offensive began, Israeli troops have attacked more than 300 Hamas targets, including 112 command centers and 95 rocket launchers, the military said. It had also found 13 tunnels from Gaza into Israel, with 31 openings.
During the same period, Hamas has fired about 160 rockets into Israel from various points in Gaza, the military said.
"There has been a limited decline in number of rockets," Buchman said. "Not a big change, but the numbers are smaller than in the past couple of days."
On the diplomatic front, U.N. Secretary General Ban Ki-moon is expected to head to the region to try to relaunch cease-fire negotiations that have so far failed to defuse the conflict.
The intensification of the fighting heightened concern about mounting Palestinian civilian casualties, even as the United States, Europe, and several influential Muslim countries expressed support for Israel's offensive to weaken the Islamist militant group Hamas.
In Washington on Friday, President Obama said he had spoken to Israeli Prime Minister Benjamin Netanyahu and affirmed strong U.S. backing for Israel's right of self-defense. But Obama said he "also made clear that the United States and our friends and allies are deeply concerned about the risks of further escalation and the loss of more innocent life."
The president said Washington has been assured that the ground offensive is aimed at reducing the threat to Israel from Hamas-built tunnels.
On Friday, Israeli forces pursued a modest operation, moving roughly 1.5 miles into the Gaza Strip and zeroing in on farming areas and the outskirts of towns to search for tunnels, a senior Israeli intelligence official with knowledge of the ground incursion told reporters in a conference call.
"Our main target for now is to find, expose and ruin as much as we can the offensive tunnels and continue to diminish, as much as we can, the launching of rockets," the Israeli intelligence official said, insisting on anonymity in accordance with military protocol.
Hundreds of Palestinian families fled their homes Friday, many carrying plastic bags filled with clothes and other possessions. About 47,000 Palestinians have sought refuge in 43 U.N. shelters, more than half that number arriving in the first 24 hours of the ground offensive, the United Nations said.
"Because it is not possible to deal with the tunnels only from the air, our soldiers are now doing so on the ground," Netanyahu said. "We chose to commence this operation after we had exhausted the other possibilities, and with the understanding that without action, the price that we would pay would be much greater."
But Netanyahu also acknowledged that "there is no guarantee of 100 percent success" in the push to destroy the tunnels.
An expansion of the ground offensive, military analysts said, could entail a broadening of the mission to seek and destroy rocket launchers, weapons infrastructure and storage facilities, and perhaps even eliminate key Hamas commanders and officials. Even as Israel has relentlessly bombarded Gaza, Hamas militants have succeeded in firing hundreds of rockets into southern and central Israel, rattling Israelis. As long as the militants possess rockets and tunnels, they remain a potent threat to Israel.
The ground incursion was Israel's first into Gaza since January 2009, when it engaged in a three-week battle with Hamas that killed more than 1,400 Palestinians and 13 Israelis.
In Washington, Obama said Secretary of State John Kerry is prepared to travel to the region to help facilitate a new cease-fire, "following additional consultations."
Mideast divisions cloud Gaza cease-fire efforts. A14.