Israeli troops have captured a strategic mountain topped with a Crusader-built castle in southern Lebanon in the deepest incursion into the country in more than a quarter-century, the military said on Sunday.

The taking of Beaufort castle, near the city of Nabatiyeh, followed days of air strikes and intense fighting in nearby villages between Israeli troops and Hezbollah militants.

The capture marked a major Israeli advance in the latest Israel-Hezbollah war, which began on March 2, when Hezbollah fired rockets into northern Israel two days after the US and Israel attacked its main backer, Iran.

Since then, Israel has launched a ground invasion, capturing dozens of Lebanese villages and towns close to the border. Hezbollah has launched thousands of missiles and drones at Israeli soldiers in southern Lebanon and northern Israel.

The Israeli push came despite a nominal ceasefire that has been in place since April 17 and just days before Lebanon and Israel hold their next round of direct talks in Washington starting Tuesday.

US Secretary of State Marco Rubio spoke to Lebanese President Joseph Aoun and Israeli Prime Minister Benjamin Netanyahu to propose a fresh path to continue ongoing negotiations, according to a US official who spoke on condition of anonymity to discuss private diplomatic conversations. Under the proposal, Hezbollah would halt all attacks on Israel and Israel would refrain from escalating military operations in the Lebanese capital of Beirut, according to the official.