* Gunmen attacked main African Union base in Mogadishu

* AU says 3 peacekeepers, 5 Islamist gunmen killed

* Al Shabaab claims responsibility, says 14 peacekeepers killed (Recasts, adds AU statement)

By Abdi Sheikh and Fiesal Omar

MOGADISHU, Dec 25 (Reuters) - Eight Islamist gunmen infiltrated the main African Union (AU) base in Mogadishu on Thursday and killed three peacekeepers and a civilian contractor, the AU mission in Somalia said.

Somali militant group al Shabaab claimed responsibility for the attack, which lasted several hours, and said it had killed 14 peacekeepers. Witnesses reported hearing bomb blasts and volleys of gunfire through the day.

"We targeted the enemies at a time they were celebrating Christmas," Sheikh Abdiasis Abu Musab, al Shabaab's military operations spokesman, told Reuters.

In the past, al Shabaab has exaggerated the number of soldiers it has killed, while officials have played down losses.

The al Qaeda-aligned militants want to topple the Western-backed Mogadishu government and describe AU troops as "Christian enemies". The Islamist group also wants to impose its own strict version of sharia law in the country.

The raid showed al Shabaab's ability to carry out high-profile attacks in the capital even as it is losing territory in rural areas to AU peacekeepers who have launched two major offensives this year.

"The terrorists, some of whom were disguised in Somali National Army uniforms, breached the base camp around lunch hour and attempted to gain access to critical infrastructure, during which five of them were killed and three others captured," the AU peacekeeping mission in Somalia, AMISOM, said in a statement.

It did not disclose the nationalities of the peacekeepers and civilian contractor killed in the attack.

The AU's Halane base is on the edge of the Mogadishu international airport compound, which houses the base for U.N. operations in Somalia as well as the British and Italian embassies and has a tight security cordon and blast walls.

Western diplomats who were celebrating Christmas in the sweltering Mogadishu heat were evacuated to safety bunkers until the raid was over.

Aleem Siddique, spokesman for the United Nations in Somalia, said all U.N. staff were safe and accounted for.

Al Shabaab was pushed out of Mogadishu in 2011 but it still controls chunks of the countryside in south and central Somalia. This year it has lost several key towns, including the port city of Barawe, during the two AMISOM offensives. (Reporting by Abdi Sheikh and Feisal Omar; Writing by Drazen Jorgic; Editing by Ruth Pitchford and Pravin Char)