The sources gave no further details on Tuesday on the extent of the advance beyond the so-called "Yellow Line".
The line, separate from the UN-demarcated "Blue Line" marking the frontier between Lebanon and Israel after Israel's withdrawal in 2000, forms part of a proposed buffer zone extending 5km to 10km into southern Lebanon, where Israeli troops continue to operate in dozens of largely abandoned villages.
The move came amid escalating cross-border hostilities despite the ceasefire declared weeks ago.
Israeli Prime Minister Benjamin Netanyahu said on Monday Israel would intensify strikes against Hezbollah, while a US official said the Iran-backed group had ignored warnings to halt attacks that risked undermining negotiations to end the US-Israeli war on Iran.
Hezbollah said on Tuesday it had targeted Israeli forces advancing toward the southern Lebanese town of Zawtar al-Sharqiya with explosive drones, rockets and artillery, while the Israeli military struck several towns in southern Lebanon and the Bekaa Valley and issued new evacuation warnings.
Lebanon's health ministry says the cumulative toll from the Israeli offensive since March 2 had reached 3213 dead and 9737 wounded by May 26, while the Israeli military says Hezbollah has launched explosive drones toward Israeli troops and northern Israeli towns, killing at least 11 soldiers since the ceasefire.
The World Health Organization has said at least 608 people in Lebanon have been killed in Israeli attacks since the truce. Hezbollah has not released figures for its own casualties.
