BEIRUT (AP) — Israeli ground forces reached their deepest point in Lebanon since they invaded six weeks ago before pulling back Saturday after battles with Hezbollah militants, Lebanese state media reported.The clashes and further Israeli bombardment came as Lebanese and Hezbollah officials study a draft proposal presented by the U.S. on ending the war.Israeli troops briefly captured a strategic hill in the southern village of Chamaa, about 5 kilometers (3 miles) from the border, the state-run National News Agency reported. It said Israeli troops blew up the Shrine of Shimon the Prophet in Chamaa as well as several homes, but that could not be verified.Israel's military did not respond to requests for comment but said in a statement its troops continue “limited, localized” operations in southern Lebanon.Israeli warplanes pounded Beirut’s southern suburbs known as Dahiyeh, a Hezbollah stronghold, and several other areas including the port city of Tyre. An airstrike on the northeastern village of Khraibeh killed a couple and their four children, the National News Agency said.Shrapnel from a strike in Dahiyeh wounded a teenage girl in the head and she was in intensive care, a hospital official said on condition of anonymity because he was not authorized to speak about patients’ conditions.Israel's military said it hit multiple Hezbollah sites.Since late September, Israel has dramatically escalated its bombardment of Lebanon, vowing to severely weaken the Iranian-backed Hezbollah and end its barrages in Israel that the militants have said are in solidarity with Palestinians during the war in Gaza.Israel's military said a synagogue was struck and two civilians hurt in a “heavy rocket barrage” by Hezbollah on Haifa, northern Israel's largest city. Police said they were lightly injured. Hezbollah said it fired missiles at five Israeli military facilities in Haifa and its suburbs. Israel said Hezbollah fired more than 60 projectiles into Israel on Saturday.More than 3,400 people have been killed in Lebanon by Israeli fire — 80% of them in the past eight weeks — according to Lebanon’s Health Ministry. Israel has said it wants to ensure that thousands of Israelis can return to their homes near the border.Israel’s military said a soldier died in combat in southern Lebanon on Friday.Meanwhile, in GazaIn Gaza, an Israeli airstrike Saturday evening on a U.N.-run school sheltering displaced people killed 10 and wounded 20, the Palestinian news agency WAFA reported. It said two missiles were fired at the Abu Assi School in the Shati refugee camp on the edge of Gaza City.Israel's military said it struck a Hamas command center in the compound.A strike on a house in Nuseirat killed at least seven, including a child and three women.The war between Israel and Hamas began after Palestinian militants stormed into Israel on Oct. 7, 2023, killing about 1,200 people — mostly civilians — and abducting 250 others.Around 100 hostages are still inside Gaza, about a third of them believed to be dead. Israelis rallied again in Tel Aviv on Saturday night to demand a cease-fire deal to return them.The Health Ministry in Gaza has said at least 43,799 Palestinians have been killed in the war. The ministry does not distinguish between civilians and combatants but has said more than half of those killed have been women and children.The U.N. Security Council’s 10 elected members on Thursday circulated a draft resolution demanding “an immediate, unconditional and permanent cease-fire” in Gaza. The U.S., Israel’s closest ally, holds the key to whether the council adopts the resolution.A search for peaceOn Friday, Lebanon’s caretaker prime minister apparently urged Iran to persuade Hezbollah to agree to a cease-fire deal with Israel, which would require the group to pull back from the border.A copy of the draft proposal presented by the U.S. earlier this week was handed over to Parliament Speaker Nabih Berri, who has been negotiating on behalf of Hezbollah, according to a Lebanese official. The official, who spoke on condition of anonymity because he was not authorized to speak about the secret talks, said Berri is expected to give Lebanon’s response on Monday.Another Lebanese politician said Hezbollah officials had received the draft and would express their opinion to Berri. The politician spoke on condition of anonymity because he was not authorized to speak to the media about the ongoing talks.The proposal is based on U.N. Security Council resolution 1701, which ended the last Israel-Hezbollah war in 2006.Berri told the pan-Arab Asharq Al-Awsat newspaper that the draft does not include any item that allows Israel to act in Lebanon if the deal is violated, saying: “We will not accept any infringement of our sovereignty."He added that Lebanon does not accept the proposal to form a committee to supervise the agreement that includes members from Western countries. A U.N. peacekeeping force already operates near the border in Lebanon.Berri said talks