* Tripoli fighting spreads to western city district
* Benghazi calm after military base falls to militias
* EU pulls out staff, following U.S. and U.N. diplomats (Adds details from Benghazi, EU evacuates staff)
By Patrick Markey
TRIPOLI, July 31 Clashes with artillery and rockets spread on Thursday into two Tripoli districts, where rival militia brigades were battling over the airport in Libya's worst fighting since the 2011 revolt that ousted Muammar Gaddafi.
Nearly 200 people have been killed since the violence erupted two weeks ago in Tripoli and also in the eastern city of Benghazi, where a coalition of Islamist militants and former rebels has overrun a major army base in the city.
Three years after the fall of Gaddafi, Libya's fragile government and nascent army have failed to impose authority on heavily armed brigades of former rebels who have become the North African country's powerbrokers.
Fighting over two weeks has driven most Western diplomats out of the Libyan capital, increasing international worries that the OPEC oil producer is sliding toward becoming a failed state just across the Mediterranean from mainland Europe.
Thuds of artillery, rockets and anti-aircraft cannons echoed across Tripoli from early Thursday morning, a day after a temporary ceasefire agreed by factions to allow firefighters to put out a huge blaze at a fuel depot hit by a rocket.
There were no immediate reports of casualties from the new exchanges. But the health ministry said on Thursday hospitals had reported 179 people killed and more than 700 wounded in fighting in the two cities since the start of violence.
Most of the fighting had been restricted to southern Tripoli where warring factions have exchanged barrages between the airport controlled by Zintan brigade fighters and enclaves allied to their Misrata brigade rivals.
Clashes with Grad rockets also broke out in the district of Seraj, Janzour, 17 km (10 miles) west of the capital, a Reuters reporter said. Local Janzour brigades have usually been aligned against Zintan in the past standoffs.
Firefighters were still working on Thursday on dousing a massive fire ignited at the fuel depot near Tripoli airport three days ago, the state-run National Oil Corporation said, without giving details of how well the blaze was under control.
Western governments hope the warring factions can reach some political agreement within the newly elected parliament that is due to hold its first session on Saturday in Tobruk, two parliamentary sources said.
Once allies in the NATO-backed war against Gaddafi, the Misrata and Zintan brigades have feuded in the past over control of parts of Tripoli since the fall of the capital. But the recent fighting is the worst in three years.
Zintanis, from the western town of Zintan, have controlled the international airport since Tripoli fell. Fighting has damaged the terminal and a control centre and has burned commercial jets parked on the tarmac.
Clashes have also complicated the situation in Benghazi, after an alliance of Islamist militants and former rebels overran a special forces base in the city, forcing the army into a retreat, local residents and army officials said.
Residents said there was little sign of army or police presence on the ground in Benghazi on Thursday, two days after Islamist fighters from Ansar al-Sharia and the coalition of former rebels, Benghazi Shura Council, overtook the base.
The militant victory was an advance for Ansar al Sharia, classified as a terrorist organisation by Washington. Ansar has been blamed by authorities for an attack on the U.S. consulate in Benghazi in 2012 in which the U.S. ambassador was killed.
Special forces have now joined up with air force units to back renegade former army General Khalifa Haftar, a former Gaddafi ally who once lived in exile in the United States and returned to fight with the rebels in the 2011 uprising.
Haftar launched a self-declared campaign against Islamist militants in Benghazi, but in recent weeks appeared to struggle to make gains, residents said. A twin suicide bombing last week showed how militants were intensifying their response.
Haftar gained support initially from many residents tired of violence and assassinations, but others rejected him as an old Gaddafi ally keen on enhancing his own power.
On Thursday, a city police station and the military base were taken by militants, and they were also holding western entrances to Benghazi, residents and local officials said.
Hundreds of families have fled their homes after a week of clashes involving warplanes and helicopter gunships.
Streets were almost empty and there was the smell of burning tires after demonstrations against militia violence. But most of Benghazi was calm.
On Wednesday night, dozens of Benghazi protesters demonstrated in several districts rejecting Ansar al-Sharia. One armed group clashed with militants, and Ansar al-Sharia briefly left one of the local hospitals under its control.
"Benghazi will not fall into the hands of these people," said Ali Salem, 27, a local resident. "Even if the army did not succeed, then we will fight them."
The European Union said on Thursday it had evacuated international staff from Tripoli because of the fighting.
"Following the deterioration of the security situation in Tripoli, the EU has decided to temporarily relocate its international staff in Tripoli to Tunisia," Michael Mann, spokesman for European Union foreign policy chief Catherine Ashton, said in an e-mailed statement.
"Our colleagues have crossed the border with Tunisia this morning," he added. He did not say how many staff were involved.
Thursday's decision by the EU follows similar steps by a majority of EU member states, the United Nations mission and others with a diplomatic presence in Tripoli, such as the United States and Turkey. (Additional reporting by Martin Santa in Brussels; Editing by Mark Heinrich)