Lebanon and Israel have resumed talks in Rome, with Israel saying it is ready to move forward with plans to withdraw troops from two areas of south Lebanon under a United States-brokered deal.

A ⁠US State Department official said on Tuesday that the talks had been positive and both sides were eager to move forward. The talks will conclude after a second day on Wednesday.

The talks at the US embassy in the Italian capital are focused on how to implement a framework agreement in June aimed at ending the war in Lebanon.

Officials said moving the talks to Rome would make it easier for both countries’ delegations to consult their governments for guidance as they negotiated.

The Lebanese presidency stated that President Joseph Aoun had instructed the Lebanese delegation ahead of the talks to demand the immediate withdrawal of Israeli forces from two designated areas in southern Lebanon before any further discussions with the Israeli delegation.

Israeli Foreign Minister Gideon Saar said his country was “ready to move forward implementing these two pilot zones”.

“I hope and tend to believe that this round of discussions in Rome will promote it,” he added.

A Lebanese diplomatic source familiar with the content of the talks told AFP that “the Lebanese army is ready to gradually take control of the localities from which the Israeli army would withdraw”.

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.

The talks come after a meeting in Washington, DC on June 26 produced an agreement that called for an end to Israel’s war on Lebanon and the disarmament of armed groups – a reference to Hezbollah. It envisaged the  deployment of Lebanese troops to the south and the progressive withdrawal of Israeli forces.

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

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.

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 war on Lebanon since March, according to Lebanon’s health ministry.

At least 32 Israeli soldiers and four Israeli civilians have been killed by Hezbollah, most of them in southern Lebanon, since Israel began its attacks.