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Israeli ground forces have reached their deepest point in Lebanon since they invaded six weeks ago, before pulling back early on Saturday after fierce battles with Hezbollah, Lebanese state media reported.

Israeli troops captured a hill in the southern Lebanese village of Chamaa, about 5 kilometers (3 miles) from the Israeli border early on Saturday, the state-run National News Agency reported. It said Israeli troops were later pushed back from the hill.

It added that Israeli troops detonated 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 claimed in a statement that its troops are "continuing their limited, localised, and targeted operational activity in southern Lebanon".Ìý The military did not immediately respond to requests for comment on the Lebanese media reports.

The push on the ground came as Israeli warplanes pounded Beirut’s southern suburbs as well as several other areas in southern Lebanon including the port city of Tyre.

The morning strike in Beirut hit an area known as Dahieh, which the Israeli military called a Hezbollah stronghold, saying its planes had hit multiple sites used by the militant group. Residents were given advance warning by Israel, and it was not immediately clear whether there were any casualties.

The increase of violence came as Lebanese and Hezbollah officials are studying a draft proposal presented by the US earlier this week on ending the war.

Since late September, Israel dramatically escalated its bombardment of Lebanon. More than 3,400 people have been killed in Lebanon by Israeli fire — 80 percent of them in the eight weeks — according to Lebanon’s Health Ministry.

On Friday, Lebanon’s caretaker prime minister apparently urged Iran to try and convince Hezbollah to agree to a cease-fire deal with Israel, which would require the group to pull back from the Israel-Lebanon border. The proposal is based on UN Security Council resolution 1701, which ended the last Israel-Hezbollah war in the summer of 2006.

A copy of the draft proposal was handed over earlier this week by the US ambassador to Lebanon 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 authorised 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, were studying it and would express their opinion on it to Berri. The politician also spoke on condition of anonymity because he was not authorised to speak to the media about the ongoing talks.

Berri told the pan-Arab Asharq Al-Awsat daily newspaper that the draft does not include any item that allows Israel to act in Lebanon if the deal is violated.

"We will not accept any infringement of our sovereignty," Berri was quoted as saying.

He added that one of the items mentioned in the draft that Lebanon does not accept is the proposal to form a committee to supervise the agreement that includes members from Western countries.

Berri added that talks are ongoing regarding this point as well as other details in the draft, adding that "the atmosphere is positive but all relies on how things will end".

There is also a push to end Israel's war in Gaza, which has killed at least 43,799 Palestinians since October 7 last year in atrocities branded as war crimes and genocide by several NGOs, world leaders and UN agencies.

The UN Security Council’s 10 elected members on Thursday circulated a draft resolution demanding "an immediate, unconditional and permanent ceasefire" in Gaza.

The US, Israel’s closest ally, holds the key to whether the UN Security Council adopts the resolution. The four other permanent members — Russia, China, Britain and France — are expected to support it or abstain.