GAZA CITY — Israeli troops uncovered more than a dozen cross-border tunnels and battled Hamas gunmen on the second day of an open-ended ground operation Saturday as the Palestinian death toll climbed to 325 and diplomats scrambled to revive ceasefire efforts.

Two Israeli soldiers — Major (res.) Amotz Greenberg, 45, and Sgt. Adar Barsano, 20 — were killed by Hamas gunmen who infiltrated via a border tunnel on Saturday morning. Military sources said the attackers had planned to kill and kidnap Israeli soldiers and civilians. The IDF deployed additional troops on the Israeli border to prevent further such attacks, and intensified its search for more tunnels.

The Israeli military said it had severely diminished the arsenal of Hamas, the Islamic terrorist group ruling Gaza, but Hamas continued to fire rockets and on Saturday staged another cross-border tunnel raid.

In the northern Gaza Strip, Palestinian officials reported intensified Israeli airstrikes, shelling and numerous civilian casualties, including a mother and four children, as dozens of wounded were rushed to a local hospital in Beit Lahiya. Gaza Health Ministry spokesman Ashraf al-Kidra said the new round of airstrikes raised the death toll from the 12-day offensive to 325 Palestinians, many of them civilians and about a fifth of them children.

Sgt. Adar Barsano, 20, from Nahariya (left) and Maj. (Res.) Amotz Greenberg, 45, from Hod Hasharon, who were killed when Hamas gunmen inflitrated into southern Israel on July 19 (photo credit: Courtesy)

Sgt. Adar Barsano, 20, from Nahariya (left) and Maj. (Res.) Amotz Greenberg, 45, from Hod Hasharon, who were killed when Hamas gunmen inflitrated into southern Israel on July 19 (photo credit: Courtesy)

In Israel, a Gaza rocket killed a 30-year-old Bedouin man near the southern city of Dimona and injured four others, said police spokesman Micky Rosenfeld, marking the second Israeli civilian casualty from the latest round of fighting. Two women and two children were injured in the attack. An Israeli soldier was killed after the start of the ground operation overnight Thursday-Friday, likely from friendly fire.

The Israeli military said that during its first 24 hours on the ground in Gaza troops had discovered 13 tunnels into Israel — some as deep as 30 meters (yards) — that could be used to carry out attacks. The military said it thwarted a second infiltration attempt through such a tunnel, killing one gunman and forcing the others to return to Gaza. Two IDF soldiers were killed, and four were injured in the attack, in which the infiltrators opened fire on Israeli troops with machine guns and anti-tank fire.

The military also said that in 12 days of fighting it has hit 2,350 targets in Gaza, including 1,100 rocket launchers.

Hamas has fired more than 1,600 rockets since the latest round of fighting began on July 8. Rocket fire continued overnight, including one that landed in a residential neighborhood in the southern Israeli city of Ashdod, causing no injuries.

Troops encountered a man who appealed for medical assistance before pulling out grenades and trying to hurl them at soldiers

“We have struck hard on the two main strategic assets of Hamas: the rockets and these tunnels,” said Israeli military spokesman Lt. Col. Peter Lerner.

Israel said it had encountered little resistance on the ground so far, and had killed about 20 militants in sporadic gunbattles. Three soldiers were wounded in overnight fighting, one seriously, the military said.

In one case, it said troops encountered a man who appealed for medical assistance before pulling out grenades and trying to hurl them at soldiers. He was shot dead. Troops also encountered a donkey with explosives strapped to it.

Casualties could mount quickly if the military moves further into urban areas.

Some 50,000 Palestinians are already staying in United Nations shelters, according to UNRWA, the U.N. refugee agency for Palestinians.

Israel launched the ground operation late Thursday after hundreds of airstrikes on the Hamas-ruled territory failed to halt unrelenting rocket fire that has increasingly targeted major Israeli cities. Al-Kidra said 75 Palestinians have been killed since the ground offensive began.

An Egyptian truce proposal was rejected by Hamas, which has ruled Gaza since 2007 and has demanded the lifting of an Israeli and Egyptian blockade as part of any cease-fire agreement.

Egyptian Foreign Minister Sameh Shukri on Saturday repeated a call for the two sides to adopt its ceasefire initiative, saying it is the only offer on the table, despite efforts from Hamas backers Turkey and Qatar to broker a deal.

“This initiative still presents the chance for the two sides to cease fire, ending the bloodshed,” he said. “It meets the needs of both sides. We will continue to propose it. We hope both sides accept it.”

In a fresh effort to broker a truce, U.N. chief Ban Ki-moon was to leave Saturday for the Middle East to help mediate the Gaza conflict. A cease-fire is “indispensable” for urgently needed humanitarian efforts to succeed, the under-secretary-general for political affairs Jeffrey Feltman told an emergency meeting of the Security Council on Friday.

Israeli officials have said the offensive could last up to two weeks. The military reported making steady progress but said dozens of tunnels remain and would not give a time frame for its operation.

Israel’s military chief, Lt. Gen. Benny Gantz, visited troops on the Gaza border early Saturday and said “a strategic national patience is necessary” to complete the mission.

“Hamas and other terror organizations have been hit hard, painfully and extensively,” he added.

“The Palestinian people in the Gaza Strip will not surrender to the enemy and will not raise the white flag,” Ziad Nakhala, a leader in the Islamic Jihad militant group, told a Palestinian radio station. “We are open to all possibilities as long as the enemy does not respond to the demands of the resistance.”

Hamas has survived Israeli offensives in the past, including a major three-week ground operation in January 2009 and another weeklong air offensive in 2012. It now controls an arsenal of thousands of rockets, including long-range projectiles, and has built a system of underground bunkers.

But Hamas is weaker than it was during the previous two offensives, with little international or even regional support from its main allies, Turkey and Qatar. Protests against the offensive took place Friday in Turkey, Jordan and the West Bank.