* Fight for Syrian military base near border spills over
* Iraq has closed border, stationed army
* Shi'ite govt in Baghdad "neutral" but fears Sunni rebels
By Patrick Markey
AL QAIM, Iraq, Sept 8 (Reuters) - Three rockets fired from Syria hit an Iraqi border town on Saturday, killing a 5-year-old girl, locals and officials said, in the most serious spillover from the neighbouring country's civil war.
As rebels fought government forces for an airfield and military base near the Syrian border town of Albu Kamal, Katyusha rockets hit a residential area of al Qaim in Iraq, smashing through a wall of one house and killing a girl inside.
"She was sitting on my lap just before we heard the rocket. I knew she was dead immediately after the explosion," said Firas Attallah, the girl's father, showing a bloodstained mattress amid the shattered glass in his home.
Baghdad said a total of four rockets were fired in what it called a "criminal operation".
"Despite the fact that Iraq is committed to adopting a neutral stance towards the crisis in Syria, our brave forces are ready to confront and respond in case of repetition of such aggression," the interior ministry said in a statement.
The Syrian war is delicate for Iraq's Shi'ite Muslim-led government. Close to Bashar al-Assad's ally, Iran, Baghdad has resisted joining calls for the Syrian leader to step down.
Iraqi leaders fear Assad's fall will bring a hostile, hardline Sunni regime to power. But they deny U.S accusations they are allowing Iran to fly weapons to Assad over Iraqi airspace.
Iraq tightened security along its border with Syria last month after its troops exchanged fire with unidentified gunmen, rockets hit a frontier patrol and Syrian army shells landed on an Iraqi border town.
The army took over frontier operations from regular border guards last month.
Local officials said they were unsure who fired the rockets.
But one Iraqi military official said it was probably rebels from the anti-Assad Free Syrian Army. He said Iraqi border troops had clashed with rebel forces two days earlier after they tried to stop smugglers getting supplies to rebels.
Al Qaim officials say more than 4,000 Syrian refugees have crossed the border which is now closed pending the construction of new camps.
Albu Kamal, site of the Syrian military base at the heart of the local battle, lies 120 km (75 miles) southeast of the city of Deir al-Zor, capital of a Sunni Muslim province with strong family and clan connections to Iraq's Sunni heartland in Anbar province.