Lebanon and Israel resumed talks on Tuesday in the Italian capital, with Beirut hoping for progress towards securing an Israeli withdrawal from south Lebanon under a US-brokered deal, although expectations for swift progress were low.

US-led diplomacy has emerged since Hezbollah and Israel returned to war on March 2 amid the wider regional conflict, moving forward despite strong objections from the Iran-backed group, which believes only Iranian pressure on Washington can secure an end to the war and Israeli withdrawal.

Iran demanded an end to the war in Lebanon as part of its interim deal with Washington signed last month, but the agreement has been shaken over the last week by renewed US-Iranian hostilities in the Gulf.

Read: Iranian army says Hormuz will never open by ‘American aggression’

Israel’s ​military is occupying what it describes as a “buffer zone” about 10 km (6 miles) into Lebanon along the entire length of the Israeli border. Israeli officials say the zone ‌is ⁠necessary to protect northern Israeli communities from attacks launched by Hezbollah.

A meeting in Washington on June 26 produced an agreement that called for an end to the Lebanon conflict, the disarmament of militant groups – an apparent reference to Hezbollah – as well as the deployment of Lebanese troops to the south and the progressive withdrawal of Israeli forces.

But deadly Israeli strikes have continued, and Hezbollah has rejected the agreement as well as efforts to disarm it. Israel, meanwhile, has said its troops would remain in southern Lebanon as long as Hezbollah remained armed.

Lebanese and Israeli officials will meet at the US embassy in Rome on Tuesday and Wednesday to set out how to implement the framework deal, Lebanese officials told Reuters. One of the officials said moving the talks to Rome would make it easier for both countries’ delegations to consult their governments for guidance as they negotiated.

Italian Foreign Minister Antonio Tajani said on Monday that Italy had offered to host the talks to continue work towards a genuine ceasefire in Lebanon.

“We are also very pleased that Rome can serve as the venue for these meetings. In this way, our capital becomes a capital of peace,” Tajani said ahead of a European Union meeting in Brussels on Monday.

Pilot zones on the table

In comments published by his office on Monday, Lebanese President Joseph Aoun said he hoped the Rome meeting would yield “tangible and practical steps on the ground” to implement the agreement and that it would see Israel begin its troop pull-out so that the Lebanese army could deploy to the south.

One of the Lebanese officials said the country’s delegation to Tuesday’s talks would seek the gradual and sequential withdrawal of Israeli troops “one zone after another,” referring to the “pilot zone” project under which Hezbollah would disarm, Israeli forces would withdraw and Lebanese troops would deploy area by area in southern Lebanon.

Read more: Lebanon, Israel to hold talks in Rome in July: Italian Foreign Ministry

The June 26 agreement said two zones had been identified as a starting point. A US official said last week that the US military’s Central Command (Centcom) was coordinating with both Lebanon and Israel to launch the pilot zones. A US military delegation was in Lebanon at the weekend to discuss the plan in detail with Lebanon’s army, sources told Reuters.

Israel’s military has forced the local Lebanese population from their homes and carried out controlled explosions of entire villages. It says it is destroying infrastructure, including underground tunnels, used by Hezbollah.

More than 4,000 Lebanese have been killed and more than a million displaced by Israel’s campaign in Lebanon since March, according to Lebanon’s health ministry. The toll does not say how many combatants may be among the dead and Hezbollah has not disclosed figures on its war dead. Reuters reported on May 3 that several thousand Hezbollah fighters had been killed.

At least 32 Israeli soldiers ​and four Israeli civilians have ​been killed by Hezbollah, most ⁠of them in southern Lebanon since the latest fighting erupted.