* Militants, army forces fight in Benghazi
* More diplomats flee chaos
* Armed brigade vows to keep fighting for Tripoli airport
By Feras Bosalum and Ahmed Elumami
BENGHAZI, Libya, Aug 1 (Reuters) - Two thousand people took to the streets of Benghazi on Friday to protest against Islamist militants and former rebel militias who have been fighting armed forces and taken over an important military base in the eastern Libyan city.
The heavy clashes in Benghazi and the capital Tripoli over the past two weeks have been the worst since the 2011 fall of Muammar Gaddafi, killing more than 200 people and forcing most Western governments to pull their diplomats out of the North African state.
Fierce fighting among rival factions in the country's two major cities also underscores Libya's fragile control over the heavily armed brigades of former anti-Gaddafi rebel fighters and militias who refuse to disband.
The Benghazi Revolutionaries Shura Council, an alliance formed by former rebels and Islamist militants from Ansar al-Sharia, which Washington classifies as a terrorist organisation, have forced the army to pull out of Benghazi.
Chanting slogans praising Libya's army and condemning extremism, protesters marched in Benghazi, the city where in 2012 the U.S. ambassador and three other Americans were killed in an attack on the U.S. mission blamed on Islamist fighters.
"We are here to say Benghazi will not become another Mosul," said Seraj Byouk, a doctor, referring to the Iraqi city which has fallen under the control of an al Qaeda splinter group.
The battle in Benghazi has pitted Islamist militants and militias against special forces who have joined ranks with a renegade former army officer, Khalifa Haftar, who had vowed to oust militants from the city.
While Haftar initially gained support from some Libyans weary of militant attacks and assassinations, he has failed to make significant gains. Critics dismiss him as a power-hungry, former Gaddafi ally.
There were no sign of the Libyan army, Haftar's forces or Shura Council forces in the city on Friday, and only civilians were controlling checkpoints and organising traffic, a Reuters reporter said.
The city's main police station was destroyed by bombs placed inside the building on Friday morning. The special forces base was empty three days after it was overrun, and other parts of the city were quiet.
Mediators including tribal leaders and elders have been trying to negotiate separate ceasefire agreements to stop the militia clashes that have turned the two biggest Libyan cities to battlefields.
Libya's new elected parliament is set to hold its first session, in the town of Tobruk on Saturday. Libya's acting prime minister, Abdullah al-Thinni, other ministers and around 100 members of parliament arrived in the eastern town on Friday.
Western governments, who have struggled to bring Libya's warring factions together, hope the parliament, known as the House of Representatives, will allow space for some form of political agreement to emerge.
But armed factions have repeatedly invaded ministries, and the last parliament, to make political demands on lawmakers, whom many Libyans blame for the lack of progress in the transition from Gaddafi's one-man rule.
MORE DIPLOMATS OUT, NO CEASEFIRE
Greece on Friday became the latest European government to take its diplomats out of Libya after fierce street battles closed the capital's international airport last month and increased worries of Libya sliding into greater chaos.
Greece evacuated its embassy staff and more than 100 other European and Chinese nationals from Libya early on Friday with a navy frigate sailing back to the Greek port of Piraeus, its Defence Ministry said.
That evacuation followed the United Nations, United States and most European nations pulling out their embassy staff and nationals from Libya, where the fragile government and fledging army are no match for militia brigades.
In Tripoli, fighting has been mainly between two rival brigades of former rebels tied to the towns of Misrata and Zintan, who have fired Grad rockets and artillery shells across southern Tripoli for two weeks in a battle to control the airport.
"The military operations aim to put an end to armed outlaw groups and bring back the state's control of all the Libyan institutions," Mohamed Ghariani, a spokesman for the Misrata forces trying to take back the airport from the Zintan brigades, told reporters.
Both Zintan and Misrata brigades claim legitimacy as state forces. They have stockpiles of Gaddafi-era weapons, and have allied themselves with competing political factions in Libya. (Additional reporting by Ayman Al-Warfalli; Writing by Aziz El-Yaakoubi; Editing by Patrick Markey and Mohammad Zargham)