Israel said further troop withdrawals from southern Lebanon would depend on the dismantling of Hezbollah, as Lebanese and Israeli negotiating teams continued a new round of U.S.-mediated talks in Rome on Wednesday aimed at advancing a phased security arrangement.

The negotiations, which began Tuesday, are focused on implementing a "pilot zones" plan that would see Israeli forces withdraw from selected areas in southern Lebanon and the Lebanese army gradually take control under U.S. supervision.

Speaking ahead of the talks, Israeli Ambassador to the United States Michael Leiter said Israel remains committed to the pilot zones initiative but made clear that any broader withdrawal would be contingent on Hezbollah's removal from the areas concerned.

"We can withdraw the moment Hezbollah is dismantled," Leiter said in an interview with CBS' Face the Nation.

"If Hezbollah is not dismantled, then we have to stay in our security zone because we're not going to go back to a situation where our citizens are threatened by an Iranian proxy firing missiles and building tunnels to carry out attacks," he added. 

Leiter said the United States, through U.S. Central Command (CENTCOM), and Lebanon are working together to establish the conditions necessary for the pilot zones to move forward.

"We're working together with CENTCOM and the Lebanese Armed Forces to create the conditions so the pilot zones can be handed over to the Lebanese army," he said. "If Hezbollah remains there, then we haven't achieved anything. That's why they're called pilot zones. If the model succeeds, we'll continue the withdrawal. If it doesn't, we'll remain where we are."

He said he hoped the first withdrawals could take place within the coming weeks.

Lebanon is seeking to accelerate Israel's withdrawal from occupied areas in the south while demonstrating that the Lebanese army can assume responsibility for broader civilian areas. Israel, meanwhile, wants to see stronger Lebanese military action against Hezbollah infrastructure in territories where the army deploys.

Officials familiar with the negotiations said the current round is intended to narrow remaining differences ahead of a broader meeting involving expanded delegations next month.

Discussions are centered on evaluating progress in the pilot zones mechanism, expanding the Lebanese army's deployment in southern Lebanon and strengthening security coordination under U.S. mediation.

The talks are part of a broader U.S. effort to stabilize the Israel-Lebanon border while reducing the influence of Hezbollah and its Iranian backers.

Leiter said the understandings being negotiated are intended to remove Iran from the equation entirely.

"What the agreement with Lebanon does is completely remove Iran from the paradigm," he said. "Iran has no role in Lebanon. Hezbollah has no role in Lebanon. Israel and Lebanon are actually seeking the same outcome: we want Hezbollah gone for our security, and they want it gone to restore their sovereignty."

On the Lebanese side, a diplomatic source familiar with the negotiations told Reuters on Tuesday that the Lebanese army is prepared to gradually assume control of villages vacated by Israeli forces.

The source's remarks came a day after the Lebanese presidency said President Joseph Aoun had instructed the Lebanese delegation to insist on the immediate start of an Israeli withdrawal from two pilot zones before moving on to broader negotiations.

Despite ongoing contacts, significant differences remain between the two sides, making this week's discussions largely preparatory for a more comprehensive round of negotiations expected next month.