GAZA CITY, Gaza Strip — Israeli bulldozers on Saturday demolished more than a dozen tunnels the military said were being used by Hamas gunmen to sneak beneath the southern border of the Jewish state and carry out attacks on its soldiers and civilians.
Palestinians reported intensified airstrikes and shelling as the death toll from Israel’s ground offensive rose to at least 342 Palestinians. Several Israelis have also died since fighting began more than 10 days ago.
Israeli soldiers uncovered 34 shafts leading into about a dozen underground tunnels, some as deep as 30 meters (yards), the military said.
Still, Palestinian gunmen disguised in Israeli uniforms managed to infiltrate Israel from Gaza using another tunnel and on Saturday killed two Israeli soldiers and injured several others, the military said. At least one Palestinian was killed in the clash.
Hamas said 12 of its fighters participated in the attack and that the group took some of the soldiers’ weapons back to their hideouts.
In two other confrontations, Palestinian gunmen jumped out of tunnels and shot at soldiers who returned fire. Two of the gunmen were killed. Another militant died when the explosive vest he was wearing went off, the military said.
In one instance, the militants were found with tranquilizers and handcuffs, indicating they ‘‘intended to abduct Israelis,’’ according to the military.
It was the second day that Palestinians had used their network of underground tunnels to penetrate Israel in the current round of fighting. Israel embarked on its ground offensive on Thursday, the same day 13 heavily armed Palestinians sneaked through a tunnel from Gaza and emerged inside Israel near a southern community. The militants were killed by an airstrike after they popped out of the tunnel.
Clashes persisted into late Saturday, with heavy fighting reported in several parts of Gaza.
Shimon Daniel, a retired brigadier general and former head of the Israeli military’s engineer corps, said the military knew that Hamas had a large number of tunnels designed to assault Israel.
‘‘I think finding 13 tunnels in such a short time is a great achievement,’’ he told Channel 10 TV.
He said demolishing the tunnels is dangerous. Troops must assume the passages are booby trapped. Soldiers first close off the area and check for additional openings. Then robots go inside to look around, he said.
After that, the tunnels are destroyed either by special explosives or by heavy equipment. It can take up to 12 hours to destroy each tunnel.
‘‘These tunnels aren’t for hiding. They are intended for large attacks in Israeli communities and army bases,’’ chief military spokesman Brig. Gen. Moti Almoz said.
Footage released by the Israeli military showed tunnels being demolished by army excavators and other equipment on the ground and by airstrikes from above.
Gaza Health Ministry spokesman Ashraf al-Kidra said the new round of airstrikes raised the death toll from the offensive to at least 342 Palestinians, many of them civilians.
In Israel, a Gaza rocket 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.
Casualties could mount quickly if the military moves deeper into urban areas.
Some 50,000 Palestinians are already staying in United Nations shelters, according to UNRWA, the U.N. refugee agency for Palestinians.
Early Saturday, Israeli tank fire killed at least five members of the Al Zawaydi family at their home in Beit Lahiya, including two children. In a separate incident, tank shell fire killed three members of the Hamooda family in their home, among them two children.
In Gaza City, two boys and a 12-month-old infant neighbor were killed Friday evening following the break of the Ramadan fast.
Israel says it is going to great lengths to avoid civilian casualties and blames them on Hamas, accusing it of firing from within residential neighborhoods and using civilians as ‘‘human shields.’’
The military said it has hit more than 2,500 targets in Gaza, including 1,100 rocket launchers, during the 12 days of fighting. It said that some 70 militants were killed and another 13 brought to Israel for questioning.
Gaza militants have fired more than 1,760 rockets at Israeli cities since July 8, the military said.
The military said also it had received intelligence reports that Palestinians had strapped explosives to animals and intended to send them toward soldiers. A donkey laden with explosives approached soldiers later on and blew up causing no injuries, it said.
Israel’s ground attack came after it became increasingly exasperated with rocket fire from Gaza, especially after Hamas rejected an Egyptian cease-fire plan earlier in the week.
Egyptian Foreign Minister Sameh Shukri on Saturday repeated a call for the two sides to adopt the cease-fire, saying it is the only offer on the table, despite efforts from Hamas backers Turkey and Qatar to broker a deal.
‘‘It meets the needs of both sides,’’ he said. ‘‘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.
Israeli officials have said the offensive could last up to two weeks or possibly longer.
Also Saturday, Egypt opened its border crossing with Gaza, admitting wounded to Egyptian hospitals and allowing aid and doctors back in.
Hamas, which has ruled Gaza since 2007, 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.Deitch reported from Jerusalem. Associated Press writers Aron Heller in Tel Aviv, Yousur Alhlou in Jerusalem, Sarah El Deeb in Cairo and Lefteris Pitarakis in Beit Lahiya, Gaza Strip, contributed to this report.