A Hezbollah statement said the group was meeting its pledge to "remove the terrorist threat at the borders of the nation" and was fighting "side by side" with the Syrian army.
The soldiers were en route to participate in an operation that began Saturday to oust Islamic State group militants from an area further north on the border, an army source told AFP.
Jreij said 20 Daesh fighters had been killed in the clashes, and 10 Lebanese soldiers wounded. At the same time, Syrian forces are advancing on the city of Deir al-Zor, 350 km.to the east, which could lead to Syria re-taking the Euphrates Valley and linking up with pro-Iranian militias in Iraq.
Lebanese President Michel Aoun (no relation to the Lebanese commander) arrived at the defence ministry early on Saturday to monitor the operation.
In 2014, Syria's war spilled over into northeastern Lebanon when Islamic State and Al-Nusra Front militants attacked the town of Arsal, when more than a dozen Lebanese soldiers were captured.
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Operations commenced before dawn, with the military striking IS positions in the eastern border areas with Syria, Brig.
A landmine exploded under one of the advancing armored vehicles of the army a day after it launched its biggest military operation yet against IS. "We are proud of our support for it as the sole defender of Lebanon".
The agreement saw around 8,000 refugees and jihadists transported to a jihadist-held area of northwestern Syria in return for the release of five captured Hizbollah fighters. Gen. Ali Qanso said at the Defense Ministry, warning of a hard battle ahead.
Though there are only about 600 militants in the 120-square-kilometre area, they are hiding in networks of caves dug into the mountains and are expected to use suicide attacks to defend their territory, he said.
However, the killing of civilians on a daily basis pushed the Syrian government to condemn the US-led coalition's "crimes" in Raqqa and urge the United Nations to dissolve the coalition.