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Four others were wounded in the clash at a security checkpoint near Baalbek in eastern Lebanon.
At least four people were killed on Saturday after a gunfight between Hezbollah members and Sunni gunmen near the Syrian border.
Four others were wounded in the clash at a Hezbollah checkpoint near the Roman archaeological site of Baalbek in eastern Lebanon.
Two Hezbollah members were killed.
The army, which said light weapons had been used, are looking for suspects.
There were reports of gunfire in the area all day despite the army presence, reported the Daily Star.
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Hezbollah has vowed to support the Syrian regime, worrying many Lebanese who believe that the country will be dragged deeper into the enduring conflict.
In poorer areas, particularly in the suburbs of the northern city of Tripoli, Syria-supporting Alawites and anti-regime Sunnis have clashed violently in recent months.
The violence is sometimes between powerful families representing their religious sect.
The shooting on Saturday began when the Sunni Shiah family, who oppose the the Syrian government, opened fire at Hezbollah members manning the checkpoint.
AFP reported that one woman and a passer-by were killed in the clash.
Several Sunni-owned shops in the area were burned after the clashes, the French news organization reported.