* At least 13 killed in violence in Benghazi, Tripoli
* Tripoli International Airport, air control closed
* Worst fighting in capital for six months (Adds rockets hit Tripoli airport control tower in 5th paragraph)
By Ayman Al-Warfalli and Feras Bosalum
BENGHAZI/TRIPOLI, Libya, July 14 (Reuters) - The United Nations on Monday pulled its staff out of Libya where at least 13 people have been killed in fighting in the eastern city of Benghazi and in Tripoli, forcing the closure of the international airport.
Security and medical sources said at least six people had been killed and 25 wounded in Benghazi in heavy fighting between security forces and rival militias since late Sunday.
Militias also clashed in the capital Tripoli on Sunday, killing at least seven people, shutting the main airport and air control centre and effectively leaving Libya with no international flights. The fighting was the worst in the capital for six months.
The U.N. mission in Libya said the closure of Tripoli International Airport and the deteriorating security situation made it impossible to fulfil its work.
Several Grad rockets hit the airport, damaging the control tower, a Libyan official said. A Reuters reporter at the airport heard anti-aircraft guns and other heavy weapons. Rival militias have been fighting for control of the airport since Sunday. Residents earlier said a Grad rocket struck the airport perimeter late on Monday. No further details were available.
Three years after the fall of Muammar Gaddafi, Libya has slipped deeper into chaos with its weak government and new army unable to control brigades of former rebel fighters and militias who often battle for political and economic power.
In Benghazi, irregular forces loyal to renegade former general Khalifa Haftar bombarded Islamist militia bases as part of his campaign to oust militants, and special forces also clashed with militia fighters in the city.
Most of the dead and injured were civilians, according to security and medical sources at Benghazi hospital. At least 10 houses were hit with missiles and government offices and banks were forced to close.
Tripoli airport and Misrata city airport were closed on Monday which, along with the closure two months ago of Benghazi airport, leaves the country with only a land route to Tunisia, a flashback to the 1990s when Libya was under U.N. sanctions.
The Tripoli air control centre covering western Libya was closed because it was not safe for staff to go to work, aviation officials and state news agency Lana said on Monday. The control centre is responsible for traffic in Tripoli, Misrata and Sabha.
That leaves only the tiny Labraq and Tobruk airports in the east, with few international connections, open for traffic. People living in western Libya must make an arduous road journey to Tunisia.
Western powers fear chaos in Libya will allow arms and militants to flow across its borders. The south of the vast desert country has become a haven for Islamist militants kicked out of Mali by French forces earlier this year. (Reporting by Ayman al-Warfalli, Feras Bosalum and Ulf Laessing; Writing by Patrick Markey; Editing by Janet Lawrence and James Dalgleish)