Operation comes as Hezbollah launches similar action with the Syrian army; the Lebanese forces deny any coordination
Lebanese troops launched an offensive against the Islamic State group on Saturday close to the Syrian border where the militants have been active for several years.
Simultaneously, Hezbollah, the Lebanese Shia group, and the Syrian army have announced an assault from the Syria side of the border in the western Qalamoun mountain range.
Hezbollah is deeply embroiled in the civil war that has raged in neighbouring Syria since 2011, fighting in support of President Bashar al-Assad's government.
The Lebanese army has sought to keep out of the conflict but has been forced to take action since the militants of IS and then al-Qaeda affiliate al-Nusra Front assaulted the border town of Arsal in 2014 and abducted 30 soldiers and police.
"In the name of Lebanon, in the name of kidnapped Lebanese soldiers, in the name of martyrs of the army, I announce that operation 'Dawn of Jurud' has started," army chief General Joseph Aoun said on Saturday.
He was referring to two mountainous border areas - Jurud Ras Baalbek and Jurud al-Qaa - where IS has been active.
'No fear of Daesh'
"The army is confronting the Daesh terrorists to chase them out and recover territory," army spokesman General Ali Kanso said, using an Arabic acronym for IS.
"We have no fear of Daesh."
Kanso said the army believed there were around 600 IS fighters in the two areas, controlling about 120 square kilometres of territory.
Hezbollah said it had launched a simultaneous operation against the militants from the Syrian side of the border but the army spokesman denied there had been any coordination.
"There is no coordination, not with Hezbollah or the Syrian army," Kanso said, adding that the army had started to tighten a siege of IS in the area two weeks ago.
"It's the most difficult battle so far waged by the Lebanese army against terrorist groups - the nature of the terrain and the enemy," he said, characterizing the Islamic State fighters in the area as 600 "suicide bombers".
Nine Lebanese soldiers captured during the 2014 raid are believed to remain in the hands of the militants.
Four were executed by their captors while a fifth died of his wounds. Sixteen were released in a prisoner swap in December 2015.
Last month, Hezbollah carried out a six-day offensive against IS and al-Qaeda's former affiliate in the Jurud Arsal district further south.
It ended with a ceasefire under which nearly 8,000 refugees and militants were transported to a militant-held area of northwestern Syria in return for the release of five captured Hezbollah fighters.
The evacuations were completed on Monday.
Hezbollah chief Hassan Nasrallah vowed earlier this month to clear the whole border area of militants, saying it was in the interests of both Lebanon and Syria.
Lebanon, a country of some four million people, hosts more than one million Syrian refugees.