* Fighting marks most serious spillover into Lebanon
* Sunni clerics wounded trying to enter Arsal overnight
* At least 16 Lebanese soldiers killed in Arsal fighting
By Alexander Dziadosz
BEIRUT, Aug 5 (Reuters) - Two Lebanese soldiers were killed in fighting with Islamist militants overnight in the town of Arsal on the border with Syria and an eight-year-old girl was shot dead in clashes in a northern city, security sources said on Tuesday.
The fighting in Arsal in the north of the Bekaa Valley is the most serious spillover into Lebanon from Syria's civil war since that conflict began more than three years ago.
The clashes began on Saturday after security forces arrested an Islamist commander popular with local rebels who frequently use the porous border to move in and out of Syria. Shortly after the arrest, gunmen attacked security forces in the area.
At least 16 soldiers have been killed since then and sectarian tensions have flared in Lebanon, still recovering from its own 1975-90 civil war. An unknown number of civilians and militants have also died in the fighting.
Lebanese security officials say the fighters in Arsal include members of al Qaeda's Syria branch, the Nusra Front, and an al Qaeda splinter group, the Islamic State, which has seized swathes of land in Syria and Iraq.
Fighting broke out on Monday night in Lebanon's northern port city of Tripoli after news that several Sunni clerics had been wounded as they entered Arsal to try to broker a ceasefire between the army and the militants. Men blocked several Tripoli roads on Tuesday, and most shops were closed and streets empty.
Tripoli has seen frequent fighting between local Sunni Muslims and members of the Shi'ite-derived Alawite minority. Syria's civil war has rekindled decades-old tensions.
On Tuesday, militants opened fire on a bus carrying soldiers in Tripoli, wounding at least six, security sources said.
Gunmen had also fired on several army positions throughout the port city overnight, the National News Agency said. A girl was killed when a bullet hit her in the head.
Fighting also started again in Arsal, a mainly Sunni town, around 7 a.m. (0400 GMT) as the army tried to retake a number of buildings seized by militants, the National News Agency said.
Activists and medics in the town say fighting has badly damaged the camps that are home to many of the tens of thousands of Syrian refugees estimated to live in and around the town.
While Lebanon has officially tried to distance itself from Syria's conflict, the country's powerful Shi'ite movement Hezbollah has sent fighters to aid President Bashar al-Assad, an Alawite. Assad, like Hezbollah, is backed by Shi'ite power Iran.
The rebels fighting to overthrow Assad are overwhelmingly Sunni and have received support from regional Sunni powers including Saudi Arabia.
Rocket fire, suicide attacks and gun battles connected to Syria's war have plagued Lebanon, and the conflict has worsened Lebanon's perennial political deadlock between officials divided largely along sectarian lines.
More than 170,000 people have been killed in Syria's war, which started in 2011 as a peaceful protest movement, then degenerated into civil war after a government crackdown. (Editing by Louise Ireland)