GAZA CITY (CNN) -

Gaza's night skies were illuminated Friday by clashes between Israeli forces and Hamas militants throughout the 27-mile-long Palestinian territory.

With fighting reported all along the coastal enclave, casualties poured into Gaza City's Shifaa Hospital, including children, after Israeli artillery shelled east of the city, physicians told the Hamas-run Al-Aqsa TV.

The conflict raged for a second night and came after Prime Minister Benjamin Netanyahu warned earlier in the day that ground troops are prepared to expand an offensive against Hamas militants.

Palestinian Authority President Mahmoud Abbas will travel Saturday or Sunday to Qatar, "where we're exerting every possible effort in order to do one thing: stop this bloodshed," said chief Palestinian negotiator Saeb Erakat.

"In the last 24 hours, 68 Palestinians have been killed, the infrastructure has been destroyed, more than 20,000 homes have been damaged or totally destroyed. This madness must stop," Erakat told CNN in phone interview from Turkey in the early hours of Saturday. Abbas was meeting with the Turkish Prime Minister Recep Tayyip Erdogan and spoke earlier with Pope Francis about the conflict.

"We are doing whatever we can," Erakat said.

Israeli tanks and soldiers are plunging deeper into Gaza, and the fighting against Hamas led to a high toll of casualties and a doubling of displaced Palestinians to 40,000. That prompted a U.N. relief agency to seek $60 million, authorities said.

President Barack Obama said Friday he spoke with Netanyahu and restated U.S. support for Israel's right to defend itself against Hamas rockets being fired from Gaza.

"In fact, while I was having the conversation with Prime Minister Netanyahu, sirens went off in Tel Aviv," Obama said. Those sirens sounded in response to a Hamas rocket attack on the coastal Israeli city, an Israeli government spokesman said.

But Obama also said he hoped Israel's ground assault on Gaza would continue to take an approach that "minimizes civilian casualties."

"I 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," Obama said.

The Israel Defense Forces are targeting tunnels used by Hamas and others to slip into Israel and to smuggle in weaponry and supplies.

Netanyahu did not explain what would spark a wider offensive or what it would entail. But he said Israel had no choice but to take the fight to Gaza to protect its own people.

"We chose to commence this operation after we had exhausted the other possibilities," he said, "and with the understanding that without action, the price that we would pay would be much greater."

Hamas spokesman Sami Abu Zhuri condemned the Prime Minister.

"Netanyahu is killing our children, and he will pay the price. The ground invasion is not scaring us. We pledge to drown the occupation army in Gaza's mud," Abu Zhuri said.

Four ground incursions, 90 airstrikes

The Israeli military conducted at least four ground incursions into Gaza and about 90 airstrikes, said Jeffrey Feltman, the U.N. undersecretary general for political affairs, in a briefing Friday to the U.N. Security Council.

Israel also fired 91 missiles, 357 tank shells and 150 shells from warships, Feltman said.

Hamas militants fired 127 rockets and 29 mortar shells at Israel since Thursday, Feltman said.

The Israeli military counted 135 rockets fired from Gaza since Thursday, with about 87 of them hitting Israel. One hit a kindergarten in Gan Yavne and another damaged a home in the Sha'ar HaNegev regional council.

Israeli forces struck "some 240 terror activity sites" in Gaza and found 10 tunnels with 22 exits across the territory, the military said.

Meanwhile, U.N. Secretary-General Ban Ki-moon was scheduled to travel to the region Saturday in an effort to "end the violence and find a way forward," Feltman said.

The grim task of counting casualties

The warfare between Israeli forces and Hamas militants has made for high casualties.

The Palestinian Health Ministry said that at least 271 Gaza residents have died and more than 2,000 have been injured in the territory since Israel began its military campaign against Hamas last week. At least 24 of the deaths occurred since the ground offensive started late Thursday, the ministry said.

Most of the casualties have been civilians, according to the United Nations.

Among the deaths Friday were eight members of the same Palestinian family -- including four children -- in Beit Hanoun, the Gaza Health Ministry said. The Abu Jurad family members were killed when Israeli artillery fire landed on their home in northern Gaza, the agency said.

At one point, about 20 Palestinian houses were hit in the fighting when the death toll stood at 26, Feltman said.

The IDF said early Friday that one Israeli soldier was killed by friendly fire in northern Gaza, the second Israeli fatality of the conflict. Seven soldiers were wounded.