Hezbollah's Al-Manar television and its "War Media" social media channels carried announcements of "the start of a military operation to purge Jurud Arsal and Qalamun of armed terrorists."
The operation has been anticipated for several weeks, and comes after Lebanese soldiers carrying out raids on Syrian refugee camps in the area were met with suicide bombings and a grenade attack.
On Tuesday, Prime Minister Saad Hariri said "the Lebanese army will carry out a planned-out operation in Jurud Arsal and the government gives it freedom (to do so)."
There was no official indication on Friday on whether Lebanese troops were involved in the fighting in the mountainous border region.
The official National News Agency also reported that Hezbollah fighters had launched an operation in Jurud Arsal.
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The Shiite militant group has been fighting in Syria for years alongside government troops against rebels.
The security situation in Arsal has long been a concern.
In 2014, jihadists kidnapped 30 soldiers and policemen after clashes in the area.
Four of the hostages were killed and a fifth died of his wounds, while 16 were eventually released in December 2015.
Another nine hostages are still being held.
The town of Arsal lies on the Lebanese side of the in-places ambiguously demarcated border.
Around 45,000 Syrian refugees registered with the United Nations live in the town, but more are believed to be living in camps in the Jurud area, although their numbers have not been confirmed.
The Qalamun region lies on the Syrian side of the border across from Arsal. While much of it is now under government control, pockets of rebel-held territory remain, particularly along the border.
Hezbollah media outlets said the operation had been launched on two axes -- from the Syrian town of Flita and from the southern part of Jurud Arsal, already under the group's control.
The operation comes as tensions rise in Lebanon over the presence of more than one million Syrian refugees.
Lebanese President Michel Aoun warned this week against anti-refugee rhetoric in the wake of the attacks on troops in Arsal.
After the raids, the Lebanese army arrested dozens of people, four of whom were subsequently declared to have died of pre-existing conditions while in custody.
Human rights groups have demanded an independent investigation into allegations that the four men were tortured to death.
