Israel intensified the scope of its strikes on south and east Lebanon on Tuesday despite a ceasefire, killing at least 31 people, Lebanese authorities said, as Hezbollah also kept up its attacks.

In a statement Wednesday, the Iran-backed group said its fighters "clashed with the enemy forces at point-blank range" with light and medium weapons in the town of Zawtar al-Sharqiyah, on the edge of an Israeli-declared "yellow line" in south Lebanon where its troops have been operating.

Since early Tuesday, the group had said its fighters had faced Israeli troops entering the town, which holds strategic importance due to its proximity to the major southern city of Nabatieh, just six kilometres (four miles) away.

Israel's army on Wednesday renewed an evacuation warning for Nabatieh city after issuing a similar order a day earlier, saying it would act "forcefully" against Hezbollah which it accuses of violating the ceasefire.

The Israeli troop advance towards Zawtar al-Sharqiyah comes after an Israeli military official said Tuesday that soldiers had begun operating beyond the "yellow line", which runs around 10 kilometres deep inside Lebanese territory and where residents have been warned not to return.

Israeli Prime Minister Benjamin Netanyahu also said on Tuesday that his country was intensifying operations in Lebanon.

"The (Israeli army) is operating with substantial forces on the ground and securing strategically dominant positions. We are reinforcing the security buffer zone in order to protect the communities of northern Israel," he said.