The National News Agency says the Army captured several hills between the frontier towns of Ras Baalbek and Arsal.
The militants have been a thorn in the country's side since they filtered in from neighbouring Syria in the early years of the civil war there.
The report today comes two days after the politically influential leader of the militant group Hezbollah announced the Army would lead the fight against the militants in the border region.
Hezbollah managed a campaign against al-Qaida-linked fighters also in the border region in July, leaving the Lebanese Army to take up positions behind the front lines.
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