The US envoy Amos Hochstein has said there is “positive progress” towards a ceasefire in Lebanon after talks in Beirut aimed at ending 13 months of fighting between Israel and Hezbollah. Hochstein has met Lebanese officials over the past two days after Hezbollah indicated it had agreed to the text of a US ceasefire proposal, although with some comments. He said on Tuesday that the gaps between Hezbollah and Israel had “narrowed”, raising optimism about a deal between the two parties. Hochstein will meet Benjamin Netanyahu, Israel’s prime minister, on Thursday. Fighting between Israel and Hezbollah started on 8 October 2023 after Hezbollah launched rockets at northern Israel “in solidarity” with Hamas’s attack the day before. The two sides engaged in low-grade, tit-for-tat fighting until late September, when Israel launched an intense aerial campaign across Lebanon and a ground incursion in the south. Since then, almost all of Hezbollah’s senior leadership has been killed and the group has faced continual losses on and off the battlefield. The fighting in Lebanon over the past year has killed 3,544 people, displaced 1.2 million, and destroyed swathes of south Lebanon. The World Bank said the conflict had so far cost Lebanon $8.5bn. Over the past week, Lebanese, Israeli and US officials have said that a ceasefire was increasingly possible – though the details of what that would entail are not yet clear. Central to ceasefire negotiations is the presence of Hezbollah in Lebanon’s south and its sway over the country in general, the politics of which it has dominated for the past decade. Israel has said it wants Hezbollah to be pushed back beyond the Litani River, 20 miles away from its border, as a form of security guarantee for people in northern Israel, tens of thousands of whom have been displaced by Hezbollah rocket fire over the past year. It had previously also said it wanted the power to unilaterally enforce a ceasefire agreement, which would give it de facto permission to carry out airstrikes in Lebanon at will. The Lebanese speaker of the house, Nabih Berri, said last Tuesday that “no sane person” would agree to such a condition. Israel and western mediators have pointed to an increased presence of the army in south Lebanon as a way of ensuring Hezbollah did not build up its arsenal along the border, as it did after the 2006 Israel-Hezbollah war. Hezbollah has not objected to this proposal publicly. In a speech shortly after the conclusion of Hochstein’s visit, Naim Qassem, Hezbollah’s secretary general, said the group was working on “two tracks, the field and the negotiations”, and would not stop fighting until a ceasefire was signed. He said Hezbollah would not accept any truce that allowed Israel to enter Lebanon “whenever it wants”. In the days leading up to Hochstein’s visit, Israel escalated its attacks on Lebanon, striking central Beirut three times in 24 hours after a break of more than a month. Hezbollah, in turn, launched missiles at Tel Aviv and attacked five military bases in Haifa. Initially, Hezbollah said that its purpose in attacking Israel was to force a ceasefire in Gaza – and refused to enter into negotiations before that was achieved. However, the killing of its senior leadership and thousands of its members, in addition to the continual progress Israeli forces have made in south Lebanon, has led the group to abandon a Gaza ceasefire as a prerequisite for negotiations. On Wednesday, Qassem said: “Our second battle after the battle to support Gaza began two months ago … which is to repel the comprehensive aggression against Lebanon.” As diplomatic efforts to end hostilities in Lebanon intensified, the US vetoed a UN security council vote on Wednesday demanding an “immediate, unconditional and permanent ceasefire” in Gaza because it did not explicitly link a truce to the release of hostages. Members of the council voted 14-1 in favour of the resolution, but it was not adopted owing to the US’s stance, which as a permanent member of the council can veto resolutions. A US official told Reuters that the resolution had been “cynically” designed by Russia and China to provoke a US veto after new language the US said it would support was rejected. Negotiations aimed at a lasting ceasefire in Gaza and the release of approximately 100 Israeli hostages, who are still being held by Hamas after being captured in the group’s attack on Israel last October, have repeatedly failed. Qatar announced earlier this month that it was quitting its mediation role until Israel and Hamas show “willingness and seriousness” in the talks. In Gaza, Israeli forces deepened their weeks-long push into the north, killing at least 33 people across the territory on Wednesday, according to medics. An Israeli strike killed a rescue worker as the civil defence was responding to an airstrike in the Sabra area of Gaza City. Israeli also struck a school-turned shelter in the centre of Gaza, killing three and injuring 20. The Israeli military did not immediately comment on the strikes. Israel launched a new ground and aerial offensive on northern Gaza in early October that it said was necessary to tackle regrouped Hamas cells. Sweeping evacuation orders for the 400,000 people the UN estimated remained there, the blockage of aid and food deliveries and the targeting of civilian infrastructure such as hospitals have led rights groups to accuse Israel of the war crime of seeking to forcibly displace the remaining population. Israel has denied that it is systematically removing Palestinians from the area or using food as a weapon, both illegal under international law. Almost 44,000 people have been killed in Gaza since the war began 13 months ago, according to the health ministry in Gaza.