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 of Beirut's southern suburbs, a Hezbollah stronghold, came as Lebanese and Hezbollah officials study a draft proposal presented by the U.S. earlier this week on ending the war. Israeli troops captured a strategic hill in the southern Lebanese village of Chamaa, about 5 kilometers (3 miles) from the Israeli border, the state-run National News Agency reported. It said the troops were later pushed back. The agency added that Israeli troops blew up the Shrine of Shimon the Prophet in Chamaa as well as several homes before they withdrew, but the claim could not be immediately verified. Israel's military did not immediately respond to requests for comment but said in a statement that its troops continue their limited, localized and targeted operational .