Lebanon's army says its troops have begun deploying to a "pilot zone" in the south of the country following the withdrawal of Israeli forces under a US-brokered agreement reached last month.

A statement from the army command said units had entered the village of Zawtar al-Gharbiyeh in Nabatieh district on Tuesday morning.

On Monday night, Israel's military confirmed the start of the pilot zone plan, which should see Israeli troops pulling out of a small part of the territory occupied during their conflict with Hezbollah as well as the disarmament of the Iran-backed group.

It comes ahead of a meeting in Washington between US President Donald Trump and his Lebanese counterpart, Joseph Aoun.

Aoun is expected to urge Trump to put pressure on Israel to withdraw from the rest of southern Lebanon and to provide support to the Lebanese army to take full control of areas where Hezbollah holds sway.

The US state department announced on Monday afternoon that "pilot zone operations" had begun in Zawtar al-Gharbiyeh and two other Lebanese villages, Froun and Srifa, in line with the Trilateral Framework agreement between Israel, Lebanon and the US.

It said the "milestone" was the direct result of discussions last week between Israeli and Lebanese representatives in Rome.

Later on Monday, an Israeli military official confirmed that the Israel Defense Forces (IDF) would "adjust its force posture in one of the pilot areas" to allow the Lebanese army to carry out its mission, while also "safeguarding the security of IDF soldiers and preserving its right to self-defence and to remove threats".

"The objective of the pilot and the agreement is the disarmament of the Hezbollah terrorist organisation and the removal of its illegal weapons," the official said.

They also reiterated that the IDF would remain in the "security zone" - the 10km (six-mile) deep strip of occupied Lebanese territory running along the border - for "as long as necessary" to defend northern Israeli communities.

On Tuesday, the Lebanese army's command said its units had begun deploying to Zawtar al-Gharbiyeh "based on ongoing communications with the Military Co-ordination Group for Lebanon", referring to the trilateral body created to support implementation of the framework.

The statement also called on Lebanese citizens "not to head to the village until the security situation stabilises, and to comply with the instructions of the deployed military units for their own safety".

The Lebanese army said its troops were already carrying out missions in nearby Froun and Srifa following Monday's US announcement.

An Israeli source also told the Haaretz newspaper that there were no Israeli troops in those villages.

Lebanon was drawn into the war between Israel, the US and Iran on March 2, when Hezbollah launched rockets into Israel in retaliation for a strike that killed Iran's supreme leader.

Israel responded by launching a bombing campaign across Lebanon and invading a significant part of the country's south.

More than 4,300 people have been killed in Lebanon, including almost 800 children, women and medics, according to the Lebanese health ministry.

Israeli authorities say 37 Israeli soldiers and four civilians have been killed on both sides of the border during the conflict.