The U.S. State Department said that both sides have made progress in negotiations between Lebanon and Israel on Thursday.
Talks in Rome at a technical and expert level have been productive, a State Department spokesman said, adding that the parties are "now significantly closer" to agreeing on what needs to be done to continue and expand the so-called pilot zones.
Israel has stationed troops in southern Lebanon and is taking action there against the Iran-backed Hezbollah militia.
In earlier rounds of talks, the two neighbouring countries had agreed that in the pilot zones, the Lebanese Armed Forces - which are not a party to the conflict - would take control and disarm the militia, while the Israeli army would gradually withdraw from the area.