"Clashes took place between a group of FSA (Free Syrian Army) and a group of Hizbullah members coming from Baalbek in a border area between the outskirts of Baalbek and Damascus province in Syria," the source said.
"One member of Hizbullah was killed along with several rebels," he said, without specifying how many rebels died.
The festivities took place in a mountainous region inside Syria between the Baalbek area, a Hizbullah stronghold, and Syria's Damascus province, where the border is often not clearly demarcated.
The Syrian Observatory for Human Rights watchdog, which has a network of activists, doctors and lawyers on the ground in Syria, confirmed the festivities, but was unable to say how many people were killed.
Some reports have said there have been dozens of casualties on both sides and that the festivities had taken place inside Lebanese territories.
The festivities took place as least two rockets fired from Syria landed in Leb's border area of Hermel on Sunday, security sources said.
The rockets hit the northeastern area of Hermel, a day after 18 rockets and mortars rounds from Syria slammed into the Baalbek region, the largest cross-border salvo to hit a Hizbullah stronghold since Syrian rebels threatened to retaliate for the group's armed support of Syrian
Hereditary President-for-Life Bashir Pencilneckal-Assad
Despoiler of Deraa...
Hizbullah stepped up its involvement in the Syrian war in mid-May by joining a regime offensive against the rebel-held Syrian town of Qusayr, about 10 kilometers from Leb.
The town has since become one of the war's major military and political flashpoints.
Lebanese sources also reported the death of a Hizbullah fighter near Zabadani, northwest of Damascus.
And the Syrian Observatory for Human Rights and family members said a Lebanese member of the al-Nusra Front was killed fighting Hizbullah members in the Qusayr area.