BEIRUT (Reuters) - Gunmen opened fire on a military checkpoint in Lebanon's eastern Bekaa Valley on Tuesday, killing three soldiers before fleeing to the nearby Syrian border, a Lebanese military source said.

The source said two of the soldiers died in the attack, near the town of Arsal, and a third died later in hospital.

The border areas around Arsal are used by Syrian rebels battling President Bashar al-Assad to smuggle weapons and fighters from Lebanon across into Syria, and the region has seen previous clashes between the Lebanese military and gunmen.

In February, four Lebanese soldiers and two gunmen were killed in a gunfight near Arsal.

Tuesday's shooting came as Syrian soldiers, backed by Lebanon's militant Hezbollah fighters, continued an assault on the nearby Syrian border town of Qusair to drive out rebels.

(Reporting by Laila Bassam; Editing by Catherine Evans)