(Adds description, local politicians on reasons for attack)
By Alexander Dziadosz
OUTSKIRTS OF ARSAL, Lebanon, Aug 4 (Reuters) - The Lebanese army advanced on Monday into a border town attacked by Islamists at the weekend in the most serious spillover of the three-year-old Syrian civil war into Lebanon.
The army pounded areas around the town of Arsal with artillery for a third day in a bid to expel the fighters identified by the army as members of the Nusra Front and the Islamic State, which has seized wide areas of Syria and Iraq.
Advancing soldiers found the bodies of 50 militants, a Lebanese security official said.
At least 13 soldiers have been killed in the fighting, which erupted after the Lebanese security forces arrested a Syrian Islamist rebel commander on Saturday. At least two dozen members of the Lebanese security services - both army and police - have been taken hostage or are missing.
The army has described the Islamists' incursion as a long-planned attack. Local politicians say it marks an attempt to extend the Islamic State's footprint into Lebanon.
The militants have been beaten back in the border area in the past year by Syrian government forces backed by Hezbollah, the Lebanese Shi'ite Muslim political and military movement. Some 3,000 fighters are estimated to be in the border zone.
Thick plumes of black and grey smoke billowed from the tops of the hills where Arsal lies. Intermittent bursts of gunfire could be heard from the surrounding areas as the army sent in reinforcements.
A dozen armoured personnel carriers were seen advancing towards the town, together with a similar number of other military vehicles including trucks and Humvees. Soldiers armed with assault rifles and rocket-propelled grenades sat atop the vehicles as they moved along the main road towards Arsal.
In a statement, the army said it had taken full control of a school that militants had seized during the incursion. It said a number of soldiers had been killed and wounded in the fighting, but gave no further details.
Arsal is a mainly Sunni town located on the Lebanese side of the border between Syrian government-controlled territory and Lebanese Shi'ite areas sympathetic to Hezbollah.
Lebanon has been buffeted by violence linked to the Syrian war including rocket attacks, suicide bombings and gun battles. But this weekend's incursion by hardline Sunni militants was the first of its kind.
More than 100,000 Syrian refugees are estimated to be living in and around Arsal. Syrian activists in the area say refugee camps have been heavily damaged during the fighting.
"The humanitarian situation is very bad. There is no place of refuge for the refugees," said one Syrian activist in the area reached by text message. "The residents are terrified."
A Syrian doctor in Arsal said on Sunday that 17 civilians had been killed.
The war in Syria has exacerbated divisions between Shi'ite Lebanese allied to the Assad government and Sunnis who have mostly been supportive of the uprising against him. Political divisions have left the country without a president since May.
Lebanon's most influential Sunni politician, former prime minister Saad al-Hariri, said Arsal must be "liberated" from the militants who he said must leave the town.
"They have no choice but to withdraw from the town and neither the state, nor we, will stand idle in the face of the plots of these groups," Hariri said in comments to the London-based Al-Hayat newspaper.
Hezbollah said on Sunday that it stood "shoulder to shoulder" with the military as it confronted what it said was a threat to the "unity, sovereignty and stability" of Lebanon.
Its forces are deployed in the area near Arsal but the group has not said whether they are taking part in the fighting. (Writing/additional reporting by Tom Perry; Editing by Peter Graff and Paul Taylor)