The unidentified assailants shot dead "two members of the Jaafar family, an Amhaz family member and a Turk" in an ambush while they were smuggling fuel through the Qaa area, he told AFP, asking not to be named.
He had initially identified the victims as four Lebanese and said a fifth man was seriously wounded.
But he revised the account to identify the fourth man killed as a Turk with a Lebanese mother, a resident of eastern Lebanon's Bekaa Valley.
Tensions were running high in the wake of the incident, the source said, with armed members of the Jaafar family gathering around five kilometres (three miles) from the mainly Sunni town of Arsal.
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Sunni residents of the area, in a statement received by AFP, condemned "this attack on honourable members of the region... That aims to sow sectarian discord".
"We disassociate ourselves from the perpetrators of this massacre whatever their identity," they said, urging the authorities to hunt down the assailants.
An army statement said it had increased patrols in the area and called for calm, saying it would "allow no one to exploit this unfortunate incident and threaten national unity".