Lebanon's army vowed to battle "terrorism" hours after a suicide bomber killed three soldiers at a checkpoint in the east near the border with war-torn Syria.

"The army knows that it is now more than ever targeted by terrorists who want to prevent the establishment of the authority of the state and its attempts to eliminate discord," the military said in a statement issued late on Saturday.

It came as a new security plan came into effect on Sunday aimed at quelling spillover violence from the conflict in Syria.

Lebanon's north and east have seen clashes between those who support the rebellion against Syria's President Bashar al-Assad and those who back Damascus.

The army command "will continue to fight and pursue terrorists, and is determined to implement the security plan... whatever the sacrifices", the statement said.

Late on Saturday the three soldiers were killed when a suicide bomber detonated his vehicle at a checkpoint at Aqabet al-Jurd in the Arsal region.

Arsal, near the border with Syria, is a Sunni town where residents support the rebels fighting Assad's forces. The town also hosts tens of thousands of Syrian refugees.

Saturday's attack was claimed on Twitter by a shadowy group calling itself Liwa Ahrar al-Sunna -- Arabic for the Brigades of the free Sunni Muslims -- which also vowed more attacks.

"The next few days will see several jihadist and blessed attacks like this one. This is only the beginning," the group said, adding that the army would be among its targets.

It said Saturday's attack was to avenge the death of Sami al-Atrash, wanted in connection with car bombings targeting Lebanon's Shiite militant group Hezbollah which has been fighting alongside Assad's forces.

Atrash was killed on Thursday in a shootout with the army in Arsal.

Hezbollah's participation in the Syria conflict has raised sectarian tensions in Lebanon.

The Arsal bombing was the second such suicide attack targeting Lebanon's military since an attack on February 22 killed two soldiers and a civilian, again in the east of the country.

Extremist groups accuse the army of discriminating against Sunnis who back the Syria uprising and of turning a blind eye to Hezbollah sending fighters across the border.

Hezbollah bastions inside Lebanon have been the target of several bloody attacks since last summer, claimed by extremist Sunnis who say the attacks are a response to the group's involvement in Syria.